![Chapter 1
Social Network Analysis: History, Concepts,
and Research
Mingxin Zhang
1.1 Introduction
Social network analysis (SNA), in essence, is not a formal theory in social science,
but rather an approach for investigating social structures, which is why SNA is often
referred to as structural analysis [1]. The most important difference between social
network analysis and the traditional or classic social research approach is that the
contexts of the social actor, or the relationships between actors are the first consid-
erations of the former, while the latter focuses on individual properties. A social
network is a group of collaborating, and/or competing individuals or entities that
are related to each other. It may be presented as a graph, or a multi-graph; each
participant in the collaboration or competition is called an actor and depicted as a
node in the graph theory. Valued relations between actors are depicted as links, or
ties, either directed or undirected, between the corresponding nodes. Actors can be
persons, organizations, or groups – any set of related entities. As such, SNA may
be used on different levels, ranging from individuals, web pages, families, small
groups, to large organizations, parties, and even to nations.
According to the well known SNA researcher Lin Freeman [2], network analy-
sis is based on the intuitive notion that these patterns are important features of the
lives of the individuals or social entities who display them; Network analysts believe
that how an individual lives, or social entity depends in large part on how that they
are tied into the larger web of social connections/structures. Many believe, more-
over, that the success or failure of societies and organizations often depends on the
patterning of their internal structure.
With a history of more than 70 years, SNA as an interdisciplinary technique de-
veloped under many influences, which come from different fields such as sociology,
mathematics and computer science, are becoming increasingly important across
many disciplines, including sociology, economics, communication science, and psy-
chology around the world. In the current chapter of this book, the author discusses
M. Zhang ()
School of Journalism and Communication, Wuhan University, Wuhan, China
e-mail: zhmxintop@yahoo.com.cn
B. Furht (ed.), Handbook of Social Network Technologies and Applications,
DOI 10.1007/978-1-4419-7142-5 1, © Springer Science+Business Media, LLC 2010
3](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-25-320.jpg)
![4 M. Zhang
the history of social network analysis, including its origin and development, in a
brief manner, and discusses definition, features, fundamental concepts and research
of social network analysis. In the end of this chapter, the author points out that devel-
oping and looking for new techniques and tools that resolve corresponding problems
challenging SNS research is urgent.
1.2 Social Network Analysis: Definition and Features
Social network is formally defined as a set of social actors, or nodes, members that
are connected by one or more types of relations [3]. Nodes, or network members,
are the units that are connected by the relations whose patterns researchers study.
The units are most commonly individuals, groups or organizations, but in princi-
ple any units that can be connected to other units can be studied as nodes, such
as web pages, blogs, emails, instant messages, families, journal articles, neighbor-
hoods, classes, sectors within organizations, positions, or nations [4–6]. Research in
a number of academic fields has shown that social networks operate on many levels,
from families up to the level of nations, and play a critical role in determining the
way problems are solved, organizations are run, and the degree to which individuals
succeed in achieving their goals [7].
Traditionally, mainstream social research focus exclusively on the behavior of
individuals. This approach neglects the social part or structure of human behavior;
the part that is concerned with the ways individuals interact and the influence they
have on one another [8]. However, social network analysts, take these parts as the
primary building blocks of the social world, they not only collect unique types of
data, they begin their analyses from a fundamentally different perspective than that
had been not adopted by individualist or attribute-based social science.
In social science, the structural approach, that is based on the study of interaction
among social actors is called social network analysis [8]. The relationships that
social network analysts study are usually those that link individual human beings,
since these social scientists believe that besides individual characteristics, relational
links or social structure, are necessary and indispensable to fully understand social
phenomena. Specifically, Wetherell et al. describe social network analysis as follows
[9, p. 645]:
Most broadly, social network analysis (1) conceptualizes social structure as a network with
ties connecting members and channelling resources, (2) focuses on the characteristics of
ties rather than on the characteristics of the individual members, and (3) views communities
as ‘personal communities’, that is, as networks of individual relations that people foster,
maintain, and use in the course of their daily lives.
Structural approach is not confined to the study of human social relationships.
As Freeman pointed out [8], it is present in almost every field of science. For exam-
ple, Freeman wrote that, molecular chemists examine how various kinds of atoms
interact together to form different kinds of molecules, while electrical engineers](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-26-320.jpg)
![1 Social Network Analysis: History, Concepts, and Research 5
observe how the interactions of various electronic components – like capacitors and
resistors – influence the flow of current through a circuit. And biologists study the
ways in which each of the species in an ecosystem interacts with and impinges on
each of the others.
There are different types of networks. Generally, network analysts differentiate
the following networks:
One Mode Versus Two Mode Networks. The former involve relations among a sin-
gle set of similar actors, while the latter involve relations among two different sets
of actors. An example of two mode network would be the analysis of a network con-
sisting of private, for profit organizations and their links to non-profit agencies in a
community [10]. Two mode networks are also used to investigate the relationship
between a set of actors and a series of events. For example, although people may
not have direct ties to each other, they may attend similar events or activities in a
community and in doing so, this sets up opportunities for the formation of “weak
ties” [11].
Complete/Whole Versus Ego Networks. Complete/whole or Socio-centric networks
consist of the connections among members of a single, bounded community. Rela-
tional ties among all of the teachers in a high school is an example of whole network.
Ego/Ego-centric or personal networks are referred to as the ties directly connecting
the focal actor, or ego to others, or ego’s alters in the network, plus ego’s views on
the ties among his or her alters. If we asked a teacher to nominate the people he/she
socializes with outside of school, and then asked that teacher to indicate who in that
network socializes with the others nominated, it is a typical ego network.
Social network analysis is the study of structure, because the social network ap-
proach is grounded in the intuitive notion that the patterning of social ties in which
actors are embedded has important consequences for those actors. This is the most
important feature of SNA. Early structural intuitions is seen as come from sociol-
ogists including Auguste Comte, Ferdinand Tönnies, Emile Durkheim, Sir Herbert
Spencer. Freeman argued [8] that these early sociologists all tried to specify the
different kinds of social ties that link individuals in different forms of social collec-
tivities. Thus, since they were all concerned with social linkages, they all shared a
structural perspective.
If structural intuition is looked as the driving force of social network analysis,
we could say that SNA is grounded in systematic empirical data, especially rela-
tional, or network data. Relational data is different with the traditional, attribute, or
sector data in that it used to describe and explain the relationship between two or
more social actors (individuals i and j, for example), while attribute data describe
and explain the relationship between two or more attributes of a single social ac-
tor (individuals i or j, for example). Tables 1.1 and 1.2 show relational data and
attribute data, respectively.
In the context of relational data, as Table 1.1 shows, researcher explores the struc-
ture of all the social actors (i.e., i1; j1; i2; j2 and other nodes), and the mathematical
formula could be represented as Sij D f.ij/. However, when dealing with attribute
data, researcher investigates correlation, causal, mediated, and other relationships](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-27-320.jpg)
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Table 1.1 Relational data i1 j1 i2 j2 : : :
i1 – Sj1i1 Si2i1 Sj2i1 Si1
j1 Si1j1 – Si2j1 Sj2j1 Sj1
i2 Si1i2 Sj1i2 – Sj2i2 Si2
j2 Si1j2 Sj1j2 Si2j2 – Sj2
: : : Si1 Sj1 Si2 Sj2 –
Table 1.2 Attribute data Y x1 x1 x3 x4 : : :
1 : : : : : : : : : : : : : : :
2 : : : : : : : : : : : : : : :
3 : : : : : : : : : : : : : : :
: : : : : : : : : : : : : : : : : :
N : : : : : : : : : : : : : : :
between different variables (i.e., dependent and independent variables, Y and x1; x2;
x3; x4 and other variables in Table 1.2). Y D f.x/ is mathematical formula in this
context.
The third prominent feature of SNA is it draws heavily on graphic imagery. In
the field of SNA, researchers use points to represent social actors and lines to repre-
sent linkages among them. There are two types of graphs: directed and undirected
graphs. Directed graph consists of a set of nodes and a set of links (also called arcs
or edges). A link e, is an ordered pair .i; j/ representing a connection from node i to
node j. Node i is called the initial node of link e, i D init.e/, and node j is called
the final node of the link: j D fin.e/. If the direction of a link is not important, or
equivalently, if existence of a link between nodes i and j necessarily implies the
existence of a link from j to i, we say that this network is an undirected graph.
A path from node i to node j is a sequence of distinct links .i; u1/, .u1; u2/; : : :,
.uk; j/. The length of this path is the number of links (here k C 1). An undirected
graph can be represented by a symmetrical matrix M D .mij/, where mij is equal to
1 if there is an edge between nodes i and j, and mij is 0 if there is no direct link
between nodes i and j.
Table 1.3 shows an imaginary relational data matrix. There is a line connecting
node A and node B. It is noticeable that this link is an ordered relation. Here A is
the initial node of link, while B is the final node. Using directed graph to describe
this data matrix, we will get Fig. 1.1.
However, graph showed in Fig. 1.1 is rather primitive, because it only consists
of six nodes and seven links. Figure 1.2 describes a more complex graph in a study
of China inter-provincial interactions conducted by Jonathan Zhu [6]. In this con-
text, there are 32 nodes (i.e., provinces) and numerous links between any pair of
two nodes. There links describe information and population interactions in China
mainland. It is clear that Beijing and Shanghai, the biggest cities in China, occupy
the centric position in the graph.](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-28-320.jpg)
![1 Social Network Analysis: History, Concepts, and Research 7
Table 1.3 An imaginary
relational data matrix
A B C D E F
A – 1 1 0 0 0
B 0 – 1 1 0 0
C 1 1 – 0 0 0
D 0 0 0 – 1 1
E 0 0 0 0 – 1
F 0 0 0 1 1 –
Fig. 1.1 Directed graph of relational data matrix in Table 1.3
Fig. 1.2 China inter-provincial interactions
Figure 1.3 shows a more complex graph regarding the co-citation network in
the research field of media economics [12]. In this graph, it is easy to know that
the following documents, such as Picard 89, Albarran 96, Owen/Wildman 92,
Scherer 73/90, Litman 79, Lacy 89,Bagdikian 83/00, and so on, occupy more](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-29-320.jpg)
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Fig. 1.3 Co-citation network in the research field of media economics
central positions in the network, indicating that they are more important than others.
Reflected by the number of ties in the graph, we could see that there are more links
point to them.
Freeman argued [8] that unlike many other approaches to social research, net-
work analysis has consistently drawn on various branches of mathematics both to
clarify its concepts and to spell out their consequences in precise terms. Thus, the us-
age of mathematical and/or computational models, is an important feature of SNA.
This is the fourth feature of SNA.
1.3 The Development of Social Network Analysis:
A Brief History
As stated above, early sociologists in the late 1800s, including Émile Durkheim and
Ferdinand Tönnies, are precursors of social network theory. Tönnies argued that so-
cial groups can exist as personal and direct social ties that either link individuals
who share values and belief or impersonal, formal, and instrumental social links.](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-30-320.jpg)
![1 Social Network Analysis: History, Concepts, and Research 9
Durkheim gave a non-individualistic explanation of social facts arguing that social
phenomena arise when interacting individuals constitute a reality that can no longer
be accounted for in terms of the properties of individual actors. He distinguished be-
tween a traditional society – “mechanical solidarity” – which prevails if individual
differences are minimized, and the modern society – “organic solidarity” – that de-
velops out of cooperation between differentiated individuals with independent roles
[8]. Georg Simmel, writing at the turn of the twentieth century, was the first scholar
to think directly in social network terms. His essays pointed to the nature of network
size on interaction and to the likelihood of interaction in ramified, loosely–knit net-
works rather than groups [13].
Social network as a relatively separate academic concept generated in 1920s–
1930s in the research filed of anthropology in Britain. Anthropologist Roger Brown
was the first researcher who used the term social network, implying that social struc-
ture is similar with a network and that interpersonal communication among individ-
uals resembles relationship between a node and another nesting in the network [14].
One of the line of social network analysis could be traced back to Sociomery
Method created by social psychologist Jacob Levy Moreno in 1930s, and this
method paved the way for quantitative analysis in social network approach. In the
1930s, Moreno pioneered the systematic recording and analysis of social interaction
in small groups, especially classrooms and work groups. According to Freeman [8],
in Moreno’s 1934 book, he used the term “network” in the sense that it is used to-
day. Freeman further pointed out that by 1938, then, the work of Moreno – with the
help of Jennings and Lazarsfeld—had displayed all four of the features that define
contemporary social network analysis [8].
The second line is a Harvard group led by W. Lloyd Warner and Elton Mayo,
which exhibited research effort that focused on the study of social structure in the
late 1920s. However, the Harvard effort never “took off” in Freeman’s eye, because
it never provided a general model for a structural paradigm. As a matter of fact, the
efforts at Harvard group are almost never recognized in historical reviews of social
network analysis [8].
The 1940s–1960s is called by Freeman as the Dark Ages in the history of the
development of SNA. In this period, there was no generally recognized approach
to social research that embodied the structural paradigm. Social network analysis
was still not identifiable either as a theoretical perspective or as an approach to data
collection and analysis [8].
In the 1960s–1970s, a growing number of scholars worked to combine the
different tracks and traditions. One large group was centered around Harrison
White and his students at Harvard University: Ivan Chase, Bonnie Erickson, Harriet
Friedmann, Mark Granovetter, Nancy Howell, Joel Levine, Nicholas Mullins,
John Padgett, Michael Schwartz and Barry Wellman. Freeman called it as the
Renaissance of SNA at Harvard. The Harvard school published so much important
theory and research focused on social networks that social scientists everywhere, re-
gardless of their field, could no longer ignore the idea. By the end of the 1970s, then,
social network analysis came to be universally recognized among social scientists.](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-31-320.jpg)
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According to Freeman’s statistics, Harrison White group at Harvard University
was not the only ones who could lay claim to the social network approach. On the
contrary, in the 40-year period from the late 1930s through the late 1970s, there were
at least 17 research groups or centers adopted a general social network perspective.
Of course, the developments at these groups or centers were not all independent
of one another. Those that emerged later undoubtedly drew on the work of at least
some of the earlier efforts [8].
Table 1.4 lists some founders and the most prominent researchers of SNA from
1940s through 1970s. However, it can’t provide more information regarding the
internal structure of these founders and researchers, just like the traditional so-
cial research could not discover the interaction patterns of social actors. Figure 1.4
describes the influences of parts of the above founders and researchers. When intro-
ducing the basic concepts in the next part of this chapter, we will give more detailed
explanations about this figure.
Table 1.4 Noticeable research groups in the development of SNA: 1930s–1970s
Time period Group leader Known researchers University/institution
1930s–1940s Kurt Lewin, John
French, Alex
Bavelas
Dorwin Cartwright,
Leon Festinger,
Duncan Luce
University of Iowa,
MIT, University
of Michigan
Mid 1940s Charles P. Loomis Leo Katz, Charles
Proctor,
T. N. Bhargava
Michigan State College
Late 1940s Lévi–Strauss – University of Chicago
Early 1950s Torsten Hägerstrand – Lund University
Early 1950s Nicolas Rashevsky Walter Pitts, Herbert D.
Landahl, Hyman G.
Landau, Anatol
Rapoport
University of Chicago
Mid 1950s Paul Lazarsfeld, Robert
K. Merton
James S. Coleman,
Elihu Katz, Herbert
Menzel, Peter Blau,
Charles Kadushin
Columbia University
Mid 1950s Everett M. Rogers George Barnett, James
Danowski, Richard
Farace, Peter
Monge, Nan Lin,
William Richards,
Ronald Rice
Iowa State University,
Michigan State
University
Mid 1950s Alfred Reginald
Radcliffe–Brown,
Max Gluckman
John Barnes, John
Barnes, J.Clyde
Mitchell, Elizabeth
Bott, Sigfried Nadel
Manchester University,
London School of
Economics
Late 1950s Karl Wolfgang Deutsch,
Ithiel de Sola Pool
Fred Kochen MIT
Late 1950s Linton C. Freeman,
Morris H. Sunshine
Thomas Fararo, Sue
Freeman
Syracuse University
Early 1960s Claude Flament – Paris Sorbonne
University
(continued)](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-32-320.jpg)
![1 Social Network Analysis: History, Concepts, and Research 11
Table 1.4 (continued)
Time period Group leader Known researchers University/institution
Mid 1960s Edward O. Laumann Stephen Berkowitz,
Ronald Burt, Joseph
Galaskiewicz, Alden
Klovdahl, David
Knoke, Peter
Marsden, Martina
Morris, David
Prensky, Philip
Schumm
University of Michigan
Late 1960s Peter Blau, James A.
Davis
– University of Chicago
Late 1960s Robert Mokken Jac Anthonisse, Frans
Stokman
1960s–1970s Harrison Colyer White Peter Bearman, Paul
Bernard, Phillip
Bonacich, Ronald L.
Breiger, Kathleen M.
Carley, Ivan Chase,
Bonnie Erickson,
Claude S. Fischer,
Mark Granovetter,
Joel Levine,
Siegwart M.
Lindenberg, Barry
Wellman,
Christopher Winship
Harvard University
When the concept of social network has been recognized by more and more
researchers, more contributions have been made in research methodology: more
and more measurement, data collection and analysis technologies were created and
developed to understand social construe and relationships better, and these in turn
advanced social network research.
In the 1980s, a number of sociologists began to use SNA as analytical technique
to examine social and economic phenomena. In mid 1980s, Mark Granovetter, pro-
posed the concept of “embedded-ness”, guiding SNA approach into the mainstream
social research field again. Granovetter argued that the operation of economics is
embedded in social structure, however, the core social structure is individuals’ so-
cial networks. In early 1980s, Granovetter formulated marketing network theory in
his well known article “Where Do Markets Come From?” [15].
After 1990s, SNA has been gradually associated with social capital, drawing
scholars’ attention from the field of sociology, politics, economics, communication
science, and other disciplines. Ronald Burt’s book Structural Holes is representa-
tive work of this period. Burt argues that social capital has not relationship with the
strength of ties, but with the existence of structural holes. Lin Nan, another well
known sociologist who proposed Social-resource theory, studied SNA from the so-
cial capital perspective. In the next part of this chapter, when comes to theorization
of SNA research design, the author will discuss Burt and Lin more.](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-33-320.jpg)
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Fig. 1.4 Influences on some founders of SNA [8, p.131]
1.4 Basic Concepts of Social Network Analysis
Social network is formally referred to as a set of social actors, or nodes, members
that are connected by one or more types of relations. To understand networks and
their participants, researchers should evaluate the location of actors in the network.
To measuring location of each node, one should use the concept centrality and other
related concepts. Through empirical measurement of a network, one will find var-
ious roles and groupings in a network – who are the connectors, mavens, leaders,
bridges, isolates? where are the clusters and who is in them? who is in the core of
the network? And, who is on the periphery?
In the following of this part, important concepts, such as ties, density, centrality,
cliques and other concepts will be explained.
1.4.1 Ties
Ties or links connect two and more nodes in a graph. Many human behaviors,
such as advice seeking, information-sharing, and lending money to somebody are
directed ties while co-memberships are examples of undirected ties. Directed ties
may be reciprocated, as would be the case for two people who visit one another, or
they may exist in only one direction as when only one gives emotional support to](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-34-320.jpg)
![1 Social Network Analysis: History, Concepts, and Research 13
the other [16]. Both directed and undirected ties can be measured as binary ties that
either exist or do not exist within each dyad, or as valued ties that can be stronger or
weaker, transmit more or fewer resources, or have more or less frequent contact.
1.4.2 Density
One of the most widely used, and perhaps over-used, concepts in graph theory is
that of “density”, which describes the general level of linkage among the points in a
graph. A “complete” graph is one in which all the points are adjacent to one another:
each point is connected directly to every other point. As an attempt to summarize the
overall distribution of lines, the concept of density aims to measure how far from this
state of completion the graph is [14]. The density of a graph is quantitatively defined
as the number of links divided by the number of vertices in a complete graph with
the same number of nodes. It is an indicator for the general level of connectedness
of the graph.
Density is one of the most basic measures in network analysis and one of the most
commonly used notions in social epidemiology. Some network structures are par-
ticularly advantageous for certain functions [17]. For example, dense networks are
particularly good for coordination of activity among the actors (because everyone
knows everyone’s business). In the case of Fig. 1.1, results of density measures(ego
networks) are shown in Table 1.5.
1.4.3 Path, Length, and Distance
Nodes or actors may be directly connected by a line, or they may be indirectly
connected through a sequence of lines. A sequence of lines in a graph is a “walk”,
and a walk in which each point and each line are distinct is called a path. The concept
of the path is, after those of the node and the line, one of the most basic of all graph
theoretical concepts. The length of a path is measured by the number of lines which
make it up. The distance between two nodes is the length of the shortest path (the
“geodesic”) which connects them [14].
Table 1.5 Density measures
of Fig. 1.1
Size Ties Pairs Density
A 2:00 2:00 2:00 100:00
B 3:00 2:00 6:00 33:33
C 2:00 1:00 2:00 50:00
D 3:00 2:00 6:00 33:33
E 2:00 2:00 2:00 100:00
F 2:00 1:00 2:00 50:00](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-35-320.jpg)
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actor. These networks begin from a list of included actors and include data on the
presence or absence of relations between every pair of actors. When examining all
students and their interpersonal relationship in a class [18], or a network of actors
appearing on film or television showing who has co-starred with whom [5], a whole
network approach should be applied. Generally, researchers using whole network
data frequently analyze more than one relation. When researcher adopts the whole
network perspective, he/she will inquire each social actor and all other individu-
als to collect relational data, then transforming into matrix (i.e., network data). In
this situation, emphasis on data analysis is not the nature of each relation type, but
structure of relation.
Ego-centric network data, however, focus on the network surrounding one node,
or in other words, the single social actor. Data are on nodes that share the chosen
relation(s) with the ego and on relations between those nodes. Ego network data can
be extracted from whole network data by choosing a focal node and examining only
nodes connected to this ego. Ego network data, like whole network data, can also
include multiple relations. These relations can be collapsed into single networks, as
when ties to people who provide companionship and emotional aid are collapsed
into a single support network [19]. Unlike whole network analyses, which com-
monly focus on one or a small number of networks, ego network analyses typically
sample large numbers of egos and their networks. Researchers using ego network
approach emphasize the significance of individual’s exploitation of his/her social
network for social resources. In these researchers’ view, individual’s social network
influences his/her social attitude and behavior.
When studying whole networks, researchers most frequently collect data on a
single type of node in networks where every node could conceivably be connected to
any other nodes. Most of the networks they analyze are one-mode networks. Two-
mode networks, involve relations among two different sets of actors or nodes –
typically organizations and organization members, or events and attendees. In these
two-mode networks or affiliation networks, relations consist of things such as mem-
berships or attendance at events that cannot exist between nodes of the same type:
A person can attend an event or belong to an organization, but a person cannot attend
or belong to another event or organization [20].
After deciding what kinds of networks and what kinds of relations under consid-
eration, researchers should decide to how to collect network data. Many methods
could be used, including (trace) observation, archives and historical materials anal-
ysis, survey, interview, and experiment [21,22].
When using survey to collect data, the following techniques could be consid-
ered in designing questionnaire. (1) Name generators: researchers ask respondents
to list the people with whom they share ties, and further ask the types, strength
or importance, and other characteristics of these ties. This technique is especially
suitable for ego network data. (2) Structurally selecting format: respondents are
asked to indicate the people with whom they have relations, however, the number
of the people should not larger than a threshold. For example, a probable ques-
tion may ask respondents that: In recently 6 months, whom do you interact with
(you can list five persons at the most)? (3) Indicating characteristics of network](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-38-320.jpg)
![1 Social Network Analysis: History, Concepts, and Research 17
members: researchers may ask respondents report democratic, societal, attitudinal,
and behavioral properties of their network members. (4) Position generators, which
was put forward by Lin Nan and colleagues, ask respondents to list their network
members in different social ranks.
Interview as an often used method, also helps SNA researchers to collect ego
network data. Researchers could ask respondents’ circle of friends, peer relations,
and primitive comradeship. This data collection method is also used to study social
support network.
1.5.2 Theorization in Social Network Analysis
Theorization is the basic goal of all research fields of social science. As a perspective
or a research paradigm, social network analysis takes as its starting point the premise
that social life is created primarily and most importantly by relations and the patterns
they form, and it provides a way of looking at a problem, but it does not predict
what we will see [20]. However, in the stage of research design, scholars should do
their best to carry out research with the application of related theories, and aim to
extend and modify social theories. In fact, several famous theories have been exactly
developed under the social network perspective.
Diffusion of innovations theory, DIT, explores social networks and their role
in influencing the spread of new ideas, products, and practices, etc. As Rogers’ s
book shows, many communication theories, such as the theory of two step flow of
communication, heterophily and communication channels, have been integrated in
related studies. Taking communication science as an example, in recent years, many
research articles examining the impacts of communication networks on the adop-
tion and usage of new information and communication technologies (ICTs) among
specific social groups in different cultural contexts [23–25] have been published in
top international journals, such as Information Research, Communication Research,
Journal of Computer Mediated Communication, etc.
Using a network perspective, Mark Granovetter [11] put forward the theory of the
“strength-of-weak-ties”. Granovetter found in one study that more numerous weak
ties can be important in seeking information and innovation. Because cliques have
a tendency to have more homogeneous opinions and common traits, individuals in
the same cliques would also know more or less what the other members know. To
gain new information and opinion, people often look beyond the clique to their other
friends and acquaintances. However, Bian Yanjie, a Chinese social scientist, found
that in China, personal networks (Guanxi1
) are used to influence authorities who in
1
Guanxi, used to describe a personal connection between two people in which one is able to prevail
upon another to perform a favor or service, or be prevailed upon, is a central concept in Chinese
society.](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-39-320.jpg)
![18 M. Zhang
turn assign jobs as favors to their contacts, which is a type of unauthorized activity
facilitated by strong ties characterized by trust and obligation. Bian called his theory
as Strong Ties [26].
The Small World is other example of theorization of social network research.
The idea of small world hypotheses that in a network, most nodes are not neighbors
of one another, but most nodes can be reached from every other by a small number
of hops or steps. This concept gave rise to the famous phrase “Six Degrees of Sepa-
ration”. In psychologist Stanley Milgram’s experiment, a sample of US individuals
were asked to reach a particular target person by passing a message along a chain of
acquaintances. Result shows that the average length of successful chains turned out
to be about five intermediaries or six separation steps.
After 1990s, scholars extend the theorization of social network analysis greatly,
among which the most famous were Ronald Burt’s theory of Structural Holes and
Lin Nan’s Social Capital Theory. Burt argue that the weaker connections between
groups are holes in the social structure of the market. These holes in social structure
create a competitive advantage for an individual whose relationships span the holes.
Finally, structural holes are an opportunity to broker the flow of information between
people, and control the projects that bring together people from opposite sides of
the hole.
As one of the very first scholars to undertake serious research on the social
networks foundation of social capital, Lin Nan’s studies in recent years produce uni-
versal influences around the world. Lin’s assumption is that the macro-level social
structure is a type of hierarchical structure, which is determined by the allocation
of various resources such as wealth, social status, and power [27,28]. In his famous
book Social Capital: A Theory of Social Structure and Action, Lin explains the im-
portance of using social connections and social relations in achieving goals. Social
capital as resources, accessed through such connections and relations, is critical in
achieving goals for individuals, social groups, organizations, and communities. The
framework of Lin’s social capital research consists of the following elements: social
actor’s network position, the strength of ties, resources, redound, and otherwise.
1.5.3 SNA Data Processing Tools
As stated above, since network data are different with the traditional attribute data,
social network analysts use corresponding techniques to process data collected.
Social network analysis software is used to identify, represent, analyze, visualize,
or simulate nodes and ties from various types of input data.
At the present, popular social network tools are UCINET, PAJEK, STRUC-
TURE, NETMINER, STOCNET, and others.
UCINET is developed by Steve Borgatti, Martin Everett and Lin Freeman [29].
The program is distributed by Analytic Technologies. It works in tandem with
freeware program called NETDRAW for visualizing networks, which is installed
automatically with UCINET. This type of software can process, read and write](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-40-320.jpg)
![1 Social Network Analysis: History, Concepts, and Research 19
a multitude of differently formatted text files, as well as Excel files, and handle
a maximum of 32,767 nodes (with some exceptions), although practically speaking,
many procedures get too slow around 5,000–10,000 nodes. Centrality measures,
subgroup identification, role analysis, elementary graph theory, permutation-based
statistical analysis, and other SNA measures can be performed on the software.
PAJEK, Slovene word for Spider, is an open source Windows program for
analysis and visualization of large networks having some thousands or even mil-
lions of vertices. It started development in November 1996, and is implemented
in Delphi (Pascal). It is freely available, for noncommercial use, at its homepage:
http://vlado.fmf.uni-lj.si/pub/networks/pajek/.The main goals in the design of Pajek
are to support abstraction by (recursive) factorization of a large network into several
smaller, which can be treated further using more sophisticated methods; to provide
the user with some powerful visualization tools; and to implement a selection of
efficient algorithms for analysis of large networks.
The program STRUCTURE is a free software package for using multi-locus
genotype data to investigate population structure. Its uses include inferring the pres-
ence of distinct populations, assigning individuals to populations, studying hybrid
zones, identifying migrants and admixed individuals, and estimating population al-
lele frequencies in situations where many individuals are migrants or admixed. It can
be applied to most of the commonly-used genetic markers, including SNPs, mi-
crosatellites, RFLPs and AFLPs. Furthermore, functions that STRUCTURE provide
cannot be found in other social network data processing tools.
NETMINER is an innovative software tool for Exploratory Analysis and Visual-
ization of Network Data. It can be used for general research and teaching in social
networks. This tool allows researchers to explore their network data visually and
interactively, helps them to detect underlying patterns and structures of the network.
Especially, it can be effectively applied to various business fields where network-
structural factors have great deal of influences on the performance (e.g., intra and
inter-organizationalfinancial Web criminal/intelligence informetric telecommunica-
tion distribution transportation networks). Statistically, this program supports many
standardized computer methods, including descriptive statistics, ANOVA, correla-
tion, and regression.
1.6 Summary
Social network analysis is the study of social structure. The social network analysts
are interested in how the individual is embedded within a structure and how the
structure emerges from the micro-relations between individual parts [30]. Hence,
the greatest advantage of SNA is that it considers how the communication net-
work structure of a group shapes individuals’ cognition, attitude and behavior. As
an approach to social research, SNA displays four features: structural intuition, sys-
tematic relational data, graphic images and mathematical or computational models
[8]. In its more than 70 years of history, social network analysts have developed](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-41-320.jpg)
![20 M. Zhang
a number of formal and precise ways of defining terms like “relation”, “density”,
“centrality”, “clique” and others, so that they can be applied unambiguously to data
on populations of individuals.
Recognizing that “we all connect, like a net we cannot see” [31], social net-
work analysis is more and more popular with researchers from various fields such
as sociology, mathematics, computer science, economics, communication science,
and psychology around the world. In social sciences, theorization of SNA has been
improved obviously in the recent two decades, although it had been criticized be-
fore 1980s. However, as new information and communication technologies (e.g., the
Internet, mobile phones, digital broadcast, etc.) have made the collection of social
network data much easier on a much larger scale at a much lower cost than what con-
ventional methods could offer, problems regarding the analysis and the subsequent
interpretation of the resulting data raise. Existing techniques seem to be inadequate
to handle new types of social network data that are continuous, dynamic, and multi-
level [6]. Thanks to the current situation, developing and looking for new techniques
and tools that resolve these problems should become social and engineering scien-
tists research agenda.
References
1. B. Wellman and S. D. Berkowitz (Eds). “Social Structures: A Network Approach.” Cambridge:
Cambridge University Press, 1988.
2. L. C. Freeman. “What is Social Network Analysis?” Last Update Friday, 08-Feb-2008, Avail-
able at: http://www.insna.org/sna/what.html
3. S. Wasserman and K. Faust. “Social Network Analysis: Methods and Applications.”
Cambridge: Cambridge University Press, 1994.
4. S. A. Boorman and H. C. White. “Social Structure from Multiple Networks. II. Role Struc-
tures.” American Journal of Sociology, Vol. 81, No. 6, 1976, pp. 1384–1446.
5. D. J. Watts. “Networks, Dynamics, and the Small-World Phenomenon.” American Journal of
Sociology, Vol. 105, No. 2, 1999, pp. 493–527.
6. J. J. H. Zhu. “Opportunities and Challenges for Network Analysis of Social and Behavioral
Data.” Seminar Series on Chaos, Control and Complex Networks City University of Hong
Kong, Poly U University of Hong Kong IEEE Hong Kong RA/CS Joint Chapter, 2007.
7. H. D. White, B. Wellman, and N. Nazer. “Does Citation Reflect Social Structure? Longitudi-
nal Evidence from the ‘Globenet’ Interdisciplinary Research Group.” Journal of the American
Society for Information Science and Technology, Vol. 55, No. 2, 2004, pp. 111–126.
8. L. C. Freeman. “The Development of Social Network Analysis: A Study in The Sociology of
Science.” Canada: Empirical Press Vancouver, 2004.
9. C. Wetherell, A. Plakans, and B. Wellman. “Social Networks, Kinship, and Community in
Eastern Europe.” Journal of Interdisciplinary History, Vol. 24, No. 1, 1994, pp. 639–663.
10. P. Hawe, C. Webster, and A. Shiell. “A Glossary of Terms for Navigating the Field of So-
cial Network Analysis.” Journal of Epidemiology and Community Health, Vol. 58, 2004,
pp. 971–975.
11. M. Granovetter. “The Strength of Weak Ties.” American Journal of Sociology, Vol. 78, 1973,
pp. 1360–1380.
12. M. X. Zhang. “Co-citation Network and the Structure of Paradigms in the Research Field of
Media Economics: 1999–2008.” Unpublished manuscript, 2011.
13. G. Simmel. “On Individuality and Social Forms.” Chicago: University of Chicago Press,
1908/1971.](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-42-320.jpg)
![24 M. Aida and H. Koto
social networks, we can better understand the process of service penetration and can
find a better activation method that can replace the word-of-mouth communication-
based marketing approach, for not only existing services but also future services.
In addition, a comprehensive understanding of the universal social network struc-
ture could be applied to not only communication services but also more general
commodities and services such as business and marketing strategies.
We explain here why we focus on power laws. We know that certain types of dis-
tributions (e.g., normal, Poisson, etc.) originate from randomness. Differing from
these distributions, power laws can be assumed to have deterministic causes. There-
fore, investigation of the reason of power laws is not disturbed by randomized effect,
and the cause of power laws is connected to other phenomena.
Our approach is summarized as follows. We analyze three different data sets: the
volume of traffic in the initial stage of NTT DoCoMo’s i-mode service [3], the logs
of NTT DoCoMo’s voice traffic, and the number of mixi users [9]. Hereafter, we call
these data sets as Service I, II, and III, respectively. Service I is the first Internet access
service offered over cellular phone terminals, Service II is a cellular phone service,
and Service III is the largest social networking service (SNS) in Japan. By combin-
ing these analyses we obtain three results with regard to the social networks that
underlie specific communication services. The first is the degree distribution of so-
cial networks, the second is the topological rules of social networks, and the last is
user dynamics with regard to the actions needed to join a communication service.
The first result was verified through a cross-check using different data; the logs of
voice traffic presented by KDDI’s cellular phone service [11]. We call this data set
as Service IV.
The rest of this chapter is organized as follows: Section 2.2 provides a conceptual
image of the methods available for analyzing social networks. Section 2.3 analyzes,
according to [1, 2], the data of the cellular phone service (Service I and II) to de-
rive partial information on the social network structure. The partial information so
obtained cannot completely determine the model of social networks and there is an
undetermined parameter in the model. Section 2.4 analyzes data on SNS (Service III)
users to supplement the partial information obtained in Sect. 2.3. The combined use
of both results enables us to determine the value of the parameter in the social net-
work model. The result is a social network model that is self-consistent with the
data observed from different services (Service I, II, and III). In Sect. 2.5, we verify
the validity of our social network model by using the traffic logs of a cellular phone
service that were not analyzed in earlier sections (Service IV). Section 2.6 concludes
our discussion with a brief summary.
2.2 Analysis Strategy
We use graph G.V; E/ to represent the relationship of people exchanging infor-
mation, where V is a set of nodes (people) and E is a set of links (information
exchanges) between nodes. We call G.V; E/ the social network.](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-45-320.jpg)
![26 M. Aida and H. Koto
2.3.1 Data To Be Analyzed
This subsection analyzes the data that holds the relationship between the number
of users and email traffic during the early growth period of Service I; the world’s
first Internet access service from cellular phone terminals [3]. Since Service I was
launched on February 22, 1999, the service has seen an explosive increase in the
number of users. In the first one and half years (up to August 2000) the number
of users exceeded ten million. The process by which a network service can acquire
users at such a dramatic rate offers an interesting window on the structure of social
networks and user behavior regarding hot-selling products.
This set of Service I data is useful for understanding social networks because it
has the following properties:
Since the number of Service I users increased explosively within a short period,
it can be assumed that the Service I traffic was little affected by external factors
such as a change in people’s lifestyle.
Since most cellular phones are exclusively used by their owners, traffic between
cellular phones can be regarded as information exchange between people.
Since most Service I emails are one-to-one communication, it can be assumed
that email traffic is closely related to the number of pairs of Service I users who
are exchanging information with each other.
Since the cost of sending an email is far lower than that of talking on the phone,
it can be assumed that the volume of email communication is little affected by
such external factors as the income level of the individual users.
Since the early period of the Service I had few problems with unwanted advertis-
ing emails sent to users indiscriminately, it can be assumed that almost all traffic
arose from existing social networks.
During the early expansion period, 6 months from the beginning of August 1999
to the end of January 2000, the number of Service I users increased almost threefold,
from 1,290,000 to 3,740,000. The relationship between the Web traffic (number of
Web access attempts) and the number of Service I users during this period can be
modeled as:
(Web traffic) / n; (2.1)
where n is the number of users (chart on the left in Fig. 2.2). This is self-evident
as long as the average number of Web access attempts per user is constant. Con-
versely, the fact that the above relation holds means that people’s average usage of
the Service I service did not change during this period. In other words, there is no
evidence that the earliest subscribers to the Service I were heavier users. Meanwhile,
the volume of email traffic (number of email messages) can be modeled as:
(Email traffic) / n5=3
: (2.2)
Thus, a power law applies (chart on the right of Fig. 2.2). If the volume of commu-
nication per user remained constant even as n increased, then the volume of email
traffic should be proportional to n. The fact that email traffic is proportional to n1C˛](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-47-320.jpg)
![30 M. Aida and H. Koto
From (2.3) and (2.4), we can derive
n
X
`D1
Di.`/ / n˛Cı
; .n N /: (2.6)
If this holds for any n of n N , then
Di.`/ / `˛Cı1
; .` N /: (2.7)
Here, let us consider three cases identified by the value of ˛ C ı 1. First, in the
case of ˛ C ı 1 0, Di.`/ decreases with respect to `. Therefore, Di.`/ is the
node degree of the `th earliest subscribed node in G.V; E/, and it is simultaneously
the node degree of the `th largest magnitude of node degree. This correspondence is
not so strict but is valid for accuracy in terms of observations in logarithmic charts.
Consequently, if ˛ C ı 1 0, we have
Di.`/ ' D.`/ (in terms of order); (2.8)
for ` N . This relation leads to the following results.
The node degree of social networks G.V; E/ obeys Zipf’s law where the expo-
nent is .1 ˛ ı/,
D.`/ / `.1˛ı/
; .` N /: (2.9)
People tend to subscribe to the Service I in the order of decreasing degree in
G.V; E/. In other words, people with more acquaintances tend to subscribe to
the service earlier.
This finding about the who subscribed to the Service I service first can be consid-
ered to mirror the tendency generally cited in the marketing area where people with
higher sensitivity to information (more acquaintances) are more likely to try some-
thing before it becomes known or popular.
Next, in the case of ˛ C ı 1 D 0, Di.`/ is independent of `. It is known that
if we construct an induced subgraph by selecting nodes in G.V; E/ at random, the
number of links in the induced subgraph is proportional to n2
where the number of
selected nodes is n [1]. This is independent of the structure of G.V; E/, and means
˛ D 1. From (2.2), the number of links should be proportional to n1C˛
(˛ ' 2=3).
Therefore, the assumption of ˛ C ı 1 D 0 contradicts the observed data of the
actual service.
Finally, in the case of ˛ C ı 1 0, people tend to subscribe to the Service
I in the order of increasing degree in G.V; E/. In other words, people with fewer
acquaintances tend to subscribe to the service earlier. This result contradicts our
personal experience. From the above considerations, we regard the assumption ˛ C
ı 1 0 as being valid.](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-51-320.jpg)
![2 Structure and Dynamics of Social Networks Revealed 31
log(rank order of degree)
e
e
r
g
e
d
(
g
o
l
o
)
s
t
n
e
m
e
l
e
f
gradient:
log(degree of elements)
m
e
l
e
f
o
r
e
b
m
u
n
(
g
o
l
ents)
gradient:
Fig. 2.5 Two points are extracted from data that satisfies Zipf’s law (left), and they are plotted to
give the distribution of degree (right)
If the distribution of the degree of nodes in the graph representing social networks
follows Zipf’s law, social networks can be taken as being scale-free. A scale-free
network is a graph in which the distribution of the degree of the nodes follows a
power law [6,7],
p.k/ / k
; (2.10)
where k is the degree of a node, p.k/ is the number of nodes with degree k, and
0 is a constant.
Assume that D.`/ follows a Zipf distribution with a gradient of ˇ (where
ˇ D 1 ˛ ı 0) as
D.`/ D C `ˇ
; (2.11)
where C is a constant. Consider ` and j for which D.`/ D k and D.j/ D k 1,
then
` D C1=ˇ
k1=ˇ
; j D C1=ˇ
.k 1/1=ˇ
: (2.12)
Since p.k/ is j ` when D.`/ D k,
p.k/ D C1=ˇ
n
.k 1/1=ˇ
k1=ˇ
o
' C1=ˇ
k1=ˇ 1
ˇ k
D O.k.1=ˇC1/
/: (2.13)
Hence, the graph representing social networks is a scale-free graph whose exponent,
, is
D
1
ˇ
C 1 D
1
1 ˛ ı
C 1: (2.14)](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-52-320.jpg)
![32 M. Aida and H. Koto
Assumptions
From Fig. 2.12 in Appendix A, the volume of email traffic is proportional to jEi.n/j.
From Fig. 2.2, jEi.n/j D O.n1C˛
/, .˛ ' 2=3/.
ci.n/ / n1ı
, .ı 1 ˛/.
Results
The sequence of subscription to the Service I is the sequence of the magnitude of the
degree in G.V; E/,
Di.`/ ' D.`/ (in terms order)
for ` N .
The degree of nodes obeys Zipf’s law:
D.`/ / `.1˛ı/
; .` N /:
The distribution of the degree of nodes in G.V; E/:
p.k/ D O.k
/;
D
1
1 ˛ ı
C 1
Fig. 2.6 The assumptions made in the analysis of service I data and the results
The assumptions made in the above discussion and its results are summarized in
Fig. 2.6.
Although the above discussion does not lead to a specific value for ı, ı should
satisfy ˛ C ı 1 0. The fact that ˛ C ı 1 indeed holds will be supported along
with the assumption of ci.n/ in the next section through an analysis of the Service III.
2.4 Analysis of Social Networks Based on the Number
of SNS Users
In this section, we investigate the structure of social networks G.V; E/ from a differ-
ent viewpoint, i.e., data generated by the Service III. In addition, by combining these
results with the results of our analysis of Service I data, we clarify the details of the
social network model including the verification of our assumption of the power law
of ci.n/ and the determination of the value of .
2.4.1 Analyzed Data
Service III is Japan’s largest social networking service provided by mixi, Inc. [9].
For a person to become a member of Service III, he or she needs to be invited to
join by an existing member. Although this is a system where only those invited by](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-53-320.jpg)
![2 Structure and Dynamics of Social Networks Revealed 33
0
500000
1000000
1500000
2000000
0 100 200 300 400 500 600 700
Number
of
mixi
users
Days from the start of service
1000
10000
100000
1000000
10000000
10 100 1000
Number
of
mixi
users
Days from the start of service
Fig. 2.7 Growth in the number of service III users
existing members may join, the number of users is growing rapidly due to the fact
that the mechanism of existing members inviting new people to join is functioning
well. The Service III started in February 2004. The number of users reached one
million on August 1, 2005, and two million on December 6, 2005. While it took
17.5 months for the number of users to reach one million, it took only 4 months for
the number to grow by another million. Because of the following characteristics of
the growth in the number of users, Service III data is useful for understanding social
networks.
Since the number of Service III users grew explosively over a short period of
time, it can be assumed that the process behind its growth was little affected by
external factors such as changes in peoples’ lifestyles.
Since a person needs to be invited to join by an existing member, the process of
the growth process of its popularity, i.e., number of users, is closely related to
links in social networks.
The left chart in Figure 2.7 shows the growth in the number of Service III users in
the early days of the service after launch with 600 users. The horizontal axis is the
number of days elapsed since the start of the service. The vertical axis is the number
of Service III users. The right chart is a double logarithmic chart. The lines with the
gradient of 3 are shown for reference. It was reported that the number of Service
III users grew exponentially [10]. Excluding the very early days, when the growth
depended on the initial conditions, it can be seen that the growth in the number of
users was time to the power of three.
2.4.2 Growth in the Number of SNS Users and Social Networks
Let m.t/ be the number of Service III users at time t, and assume that the following
holds:
m.t/ / t3
: (2.15)](https://image.slidesharecdn.com/23766300-250520030911-cac07f63/85/Handbook-Of-Social-Network-Technologies-And-Applications-Borko-Furht-54-320.jpg)
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Handbook Of Social Network Technologies And Applications Borko Furht
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- 6. Handbook of Social Network Technologies and Applications
- 8. Borko Furht Editor Handbook of Social Network Technologies and Applications ABC
- 9. Editor Borko Furht Florida Atlantic University Dept. of Comp. & Elect. Engin. and Comp. Sci. Glades Road 777 33431 Boca Raton Florida USA borko@cse.fau.edu ISBN 978-1-4419-7141-8 e-ISBN 978-1-4419-7142-5 DOI 10.1007/978-1-4419-7142-5 Springer New York Dordrecht Heidelberg London © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
- 10. To my first granddaughter Sophia Rolleri, who is the cutest in the world.
- 12. Preface Social networking is a concept that has been around for a long time; however, with the explosion of the Internet, social networking has become a tool for connecting people and allowing their communications in the ways that was previously impos- sible. Furthermore, the recent development of Web 2.0 has provided for many new applications such as Myspace, Facebook, Linkedin, and many others. The objective of this Handbook is to provide comprehensive guidelines on the current and future trends in social network technologies and applications. This Handbook is a carefully edited book – contributors are 82 worldwide experts in the field of social networks and their applications. The Handbook Advisory Board, comprised of 11 researchers and practitioners from academia and industry, helped in reshaping the Handbook and selecting the right topics and creative and knowl- edgeable contributors. The scope of the book includes leading edge social network technologies, in- frastructures, and communities; social media analysis, organizations, mining, and search; privacy and security issues in social networks; and visualization and appli- cations of social networks. The Handbook comprises of five parts, which consist of 31 chapters. The first part on Social Media Analysis and Organization includes chapters dealing with structure and dynamics of social networks, qualitative analysis of commercial social networks, and various topics relating to analysis and organization of social media. The second part on Social Media Mining and Search focuses on chapters on detecting and discovering communities in social networks, and mining information from social networks and related topics in social media mining and search. The third part on Social Network Infrastructures and Communities consists of chapters on various issues relating to distributed and decentralized online social networks, accessibility testing of social Websites, and understanding human behav- ior in social networks and related topics. The fourth part on Privacy in Online Social Networks describes various issues related to security, privacy threats, and intrusion detection in social networks. The fifth part on Visualization and Applications of Social Networks includes chapters on visualization techniques for social networks as well as chapters on several applications. vii
- 13. viii Preface With the dramatic growth of social networks and their applications, this Handbook can be the definitive resource for persons working in this field as re- searchers, scientists, programmers, engineers, and users. The book is intended for a wide variety of people including academicians, designers, developers, educators, engineers, practitioners, researchers, and graduate students. This book can also be beneficial for business managers, entrepreneurs, and investors. The book can have a great potential to be adopted as a textbook in current and new courses on Social Networks. The main features of this Handbook can be summarized as follows: 1. The Handbook describes and evaluates the current state-of-the-art in the field of social networks. 2. It also presents current trends in social media analysis, mining, and search as well social network infrastructures and communities. 3. Contributors to the Handbook are the leading researchers from academia and practitioners from industry. We would like to thank the authors for their contributions. Without their expertise and effort, this Handbook would never come to fruition. Springer editors and staff also deserve our sincere recognition for their support throughout the project. Boca Raton, Florida Borko Furht 2010 Editor-in-Chief
- 14. Editor-in-Chief Borko Furht is a professor and chairman of the Department of Electrical & Computer Engineer- ing and Computer Science at Florida Atlantic University (FAU) in Boca Raton, Florida. He is also director of recently formed NSF-sponsored Industry/University Cooperative Research Cen- ter on Advanced Knowledge Enablement. Before joining FAU, he was a vice president of re- search and a senior director of development at Modcomp (Ft. Lauderdale), a computer com- pany of Daimler Benz, Germany, a professor at University of Miami in Coral Gables, Florida, and a senior researcher in the Institute Boris Kidric-Vinca, Yugoslavia. Professor Furht re- ceived Ph.D. degree in electrical and computer engineering from the University of Belgrade. His current research is in multimedia systems, video coding and compression, 3D video and image systems, wireless multimedia, and Internet, cloud computing and social networks. He is presently Principal Investigator and Co-PI of several multiyear, mul- timillion dollar projects including NSF PIRE project and NSF High-Performance Computing Center. He is the author of numerous books and articles in the areas of multimedia, computer architecture, real-time computing, and operating systems. He is a founder and editor-in-chief of The Journal of Multimedia Tools and Applica- tions (Springer). He has received several technical and publishing awards and has consulted for many high-tech companies including IBM, Hewlett-Packard, Xerox, General Electric, JPL, NASA, Honeywell, and RCA. He has also served as a consul- tant to various colleges and universities. He has given many invited talks, keynote lectures, seminars, and tutorials. He served on the Board of Directors of several high-tech companies. ix
- 16. Contents Part I Social Media Analysis and Organization 1 Social Network Analysis: History, Concepts, and Research ............. 3 Mingxin Zhang 2 Structure and Dynamics of Social Networks Revealed by Data Analysis of Actual Communication Services ........................ 23 Masaki Aida and Hideyuki Koto 3 Analysis of Social Networks by Tensor Decomposition................... 45 Sergej Sizov, Steffen Staab, and Thomas Franz 4 Analyzing the Dynamics of Communication in Online Social Networks ............................................................... 59 Munmun De Choudhury, Hari Sundaram, Ajita John, and Doree Duncan Seligmann 5 Qualitative Analysis of Commercial Social Network Profiles ......................................................................... 95 Lester Melendez, Ouri Wolfson, Malek Adjouadi, and Naphtali Rishe 6 Analysis of Social Networks Extracted from Log Files...................115 Kateřina Slaninová, Jan Martinovič, Pavla Dráždilová, Gamila Obadi, and Václav Snášel 7 Perspectives on Social Network Analysis for Observational Scientific Data .................................................................147 Lisa Singh, Elisa Jayne Bienenstock, and Janet Mann 8 Modeling Temporal Variation in Social Network: An Evolutionary Web Graph Approach .......................................169 Susanta Mitra and Aditya Bagchi xi
- 17. xii Contents 9 Churn in Social Networks ...................................................185 Marcel Karnstedt, Tara Hennessy, Jeffrey Chan, Partha Basuchowdhuri, Conor Hayes, and Thorsten Strufe Part II Social Media Mining and Search 10 Discovering Mobile Social Networks by Semantic Technologies....................................................223 Jason J. Jung, Kwang Sun Choi, and Sung Hyuk Park 11 Online Identities and Social Networking...................................241 Muthucumaru Maheswaran, Bader Ali, Hatice Ozguven, and Julien Lord 12 Detecting Communities in Social Networks ...............................269 Tsuyoshi Murata 13 Concept Discovery in Youtube.com Using Factorization Method.........................................................................281 Janice Kwan-Wai Leung and Chun Hung Li 14 Mining Regional Representative Photos from Consumer- Generated Geotagged Photos................................................303 Keiji Yanai and Qiu Bingyu 15 Collaborative Filtering Based on Choosing a Different Number of Neighbors for Each User .......................................317 Antonio Hernando, Jesús Bobadilla, and Francisco Serradilla 16 Discovering Communities from Social Networks: Methodologies and Applications ...............................331 Bo Yang, Dayou Liu, and Jiming Liu Part III Social Network Infrastructures and Communities 17 Decentralized Online Social Networks .....................................349 Anwitaman Datta, Sonja Buchegger, Le-Hung Vu, Thorsten Strufe, and Krzysztof Rzadca 18 Multi-Relational Characterization of Dynamic Social Network Communities .......................................................379 Yu-Ru Lin, Hari Sundaram, and Aisling Kelliher 19 Accessibility Testing of Social Websites ....................................409 Cecilia Sik Lányi
- 18. Contents xiii 20 Understanding and Predicting Human Behavior for Social Communities ..................................................................427 Jose Simoes and Thomas Magedanz 21 Associating Human-Centered Concepts with Social Networks Using Fuzzy Sets ..................................................447 Ronald R. Yager Part IV Privacy in Online Social Networks 22 Managing Trust in Online Social Networks ...............................471 Touhid Bhuiyan, Audun Josang, and Yue Xu 23 Security and Privacy in Online Social Networks..........................497 Leucio Antonio Cutillo, Mark Manulis, and Thorsten Strufe 24 Investigation of Key-Player Problem in Terrorist Networks Using Bayes Conditional Probability ...........................523 D.M. Akbar Hussain 25 Optimizing Targeting of Intrusion Detection Systems in Social Networks ...............................................................549 Rami Puzis, Meytal Tubi, and Yuval Elovici 26 Security Requirements for Social Networks in Web 2.0..................569 Eduardo B. Fernandez, Carolina Marin, and Maria M. Larrondo Petrie Part V Visualisation and Applications of Social Networks 27 Visualization of Social Networks............................................585 Ing-Xiang Chen and Cheng-Zen Yang 28 Novel Visualizations and Interactions for Social Networks Exploration ....................................................................611 Nathalie Henry Riche and Jean-Daniel Fekete 29 Applications of Social Network Analysis...................................637 P. Santhi Thilagam 30 Online Advertising in Social Networks.....................................651 Abraham Bagherjeiran, Rushi P. Bhatt, Rajesh Parekh, and Vineet Chaoji
- 19. xiv Contents 31 Social Bookmarking on a Company’s Intranet: A Study of Technology Adoption and Diffusion ........................................691 Nina D. Ziv and Kerry-Ann White Index .................................................................................713
- 20. Contributors Malek Adjouadi Florida International University, Miami, FL, USA Masaki Aida Tokyo Metropolitan University, Tokyo, Japan, maida@sd.tmu.ac.jp Bader Ali McGill University, Montreal, Canada Aditya Bagchi Indian Statistical Institute, Kolkata, India Abraham Bagherjeiran Yahoo! Labs, Santa Clara, CA, USA Partha Basuchowdhuri Digital Enterprise Research Institute, National University of Ireland, Galway, Ireland Rushi Bhatt Yahoo! Labs, Bangalore, India Touhid Bhuiyan Queensland University of Technology, Brisbane, Australia, t.bhuiyan@qut.edu.au Elisa Bienenstock Georgetown University, Washington, DC, USA Jesús Bobadilla Universidad Politecnica de Madrid, Madrid, Spain Sonja Buchegger Royal Institute of Technology (KTH), Stockholm, Sweden, buc@csc.kth.se Jeffrey Chan Digital Enterprise Research Institute, National University of Ireland, Galway, Ireland Vineet Chaoji Yahoo! Labs, Bangalore, India Ing-Xiang Chen Telcordia Applied Research Centre - Taiwan, Telcordia Technologies, Piscataway, NJ 08854, seanchen@research.telcordia.com Kwang Sun Choi Saltlux, South Korea Munmun De Choudhury Arizona State University, Tempe, AZ, USA Leucio-Antonio Cutillo Eurecom, Sophia Antropolis, France Anwitaman Datta Nanyang Technological University, Singapore Pavla Drazdilova Technical University of Ostrava, Ostrava-Poruba, Czech Republic xv
- 21. xvi Contributors Doree Duncan-Seligmann Avaya Labs, New York, NY, USA Yuval Elovici Ben-Gurion University of the Negev, Israel, elovici@bgu.ac.il Jean-Daniel Fekete INRIA, University of Paris-Sud, 91405 Orsay Cedex, France Eduardo Fernandez Florida Atlantic University, Boca Raton, FL, USA, ed@cse.fau.edu Thomas Franz University of Koblenz-Landau, Landau, Germany Conor Hayes Digital Enterprise Research Institute, National University of Ireland, Galway, Ireland Tara Hennessy Digital Enterprise Research Institute, National University of Ireland, Galway, Ireland Antonio Hernando Universidad Politecnica de Madrid, Madrid, Spain, ahernandoe@yahoo.com D.M. Akbar Hussain Aalborg University, Aalborg, Denmark, akh@es.aau.dk Ajita John Avaya Labs, Lincroft, NJ, USA Audun Josang University of Oslo, Oslo, Norway Jason J. Jung Yeungnam University, Gyeongsan, South Korea, j2jung@gmail.com Marcel Karnstedt Digital Enterprise Research Institute, National University of Ireland, Galway, Ireland Aisling Kelliher Arizona State University, Tempe, AZ, USA Hideyuki Koto KDDI R&D Laboratories, Saitama, Japan Cecilia Sik Lanyi University of Pannonia, Veszprem, Hungary, lanyi@almos.uni-pannon.hu Maria Larrondo-Petrie Florida Atlantic University, Boca Raton, FL, USA Janice Kwan-Wai Leung Hong Kong Baptist University, Hong Kong, janice@Comp.HKBU.Edu.HK Chun Hung Li Hong Kong Baptist University, Hong Kong Yu-Ru Lin Arizona State University, Tempe, AZ, USA Dayou Liu Jilin University, Changchun, China Jiming Liu Hong Kong Baptist University, Hong Kong Julien Lord McGill University, Montreal, Canada Thomas Magedanz Fraunhofer Fokus, Berlin, Germany Muthucumaru Maheswaran McGill University, Montreal, Canada, maheswar@cs.mcgill.ca
- 22. Contributors xvii Janet Mann Georgetown University, Washington, DC, USA Mark Manulis TU Darmstadt & CASED, Darmstadt, Germany Carolina Marin Florida Atlantic University, Boca Raton, FL, USA Jan Martinovic Technical University of Ostrava, Ostrava, Czech Republic Laster Melendez Florida International University, Miami, FL, USA Susanta Mitra Meghnad Saha Institute of Technology, Kolkata, India, susanta mitra@yahoo.com Tsuyoshi Murata Tokyo Institute of Technology, Tokyo, Japan, murata@cs.titech.ac.jp Gamila Obadi Technical University of Ostrava, Ostrava, Czech Republic Hatice Ozguven McGill University, Montreal, Canada Rajesh Parekh Yahoo! Labs, Santa Clara, CA, USA, rparekh@yahoo-inc.com Sung-Hyuk Park KAIST Business School, Seoul, South Korea Rami Puzis Ben-Gurion University of the Negev, Beersheba, Israel, faramir.p@gmail.com Bingyu Qiu The University of Electro-Communications, Chofu-shi, Tokyo, Japan Naphtali Rishe Florida International University, Miami, FL, USA, ndr@acm.org, rishe@cs.fiu.edu Nathalie Henry Riche Microsoft Research, Redmond, WA, USA, Nathalie.Henry@microsoft.com Krzysztof Rzadca Nanyang Technological University, Singapore Francisco Serradilla Universidad Politecnica de Madrid, Madrid, Spain Jose Simoes Fraunhofer Fokus, Berlin, Germany, jose.simoes@fokus.fraunhofer.de Lisa Singh Georgetown University, Washington, DC, USA, singh@cs.georgetown.edu Sergej Sizov University of Koblenz-Landau, Koblenz, Germany, sizov@uni-koblenz.de Katerina Slaninova Technical University of Ostrava, Ostrava, Czech Republic and Silesian University of Opava, Opava, Czech Republic, slaninova@opf.slu.cz Vaclav Snasel Technical University of Ostrava, Ostrava, Czech Republic Steffen Staab University of Koblenz-Landau, Koblenz, Germany Thorsten Strufe TU Darmstadt & CASED, Darmstadt, Germany, strufe@cs.tu-darmstadt.de
- 23. xviii Contributors Hari Sundaram Arizona State University, Tempe, AZ, USA, Hari.Sundaram@asu.edu P. Santhi Thilagam National Institute of Technology Karnataka, Surathkal, Karnataka, India, santhi soci@yahoo.co.in Meytal Tubi Ben-Gurion University of the Negev, Beersheba, Israel Le Hung Vu Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland Kerry-Ann White Polytechnic Institute of New York University, New York, NY, USA Ouri Wolfson University of Illinois, Chicago, IL, USA Yue Xu Queensland University of Technology, Brisbane, Queensland, Australia Ronald R. Yager Iona College, New Rochelle, NY, USA, yager@panix.com Keiji Yanai The University of Electro-Communications, Chofu-shi, Tokyo, Japan, yanai@cs.uec.ac.jp Bo Yang Jilin University, Changchun, China, ybo@jlu.edu.cn Cheng-Zen Yang Yuan Ze University, Chungli, Taiwan Mingxin Zhang Wuhan University, Wuhan, China, zhmxintop@yahoo.com.cn Nina D. Ziv Polytechnic Institute of New York University, New York, NY, USA, nziv123@gmail.com
- 24. Part I Social Media Analysis and Organization
- 25. Chapter 1 Social Network Analysis: History, Concepts, and Research Mingxin Zhang 1.1 Introduction Social network analysis (SNA), in essence, is not a formal theory in social science, but rather an approach for investigating social structures, which is why SNA is often referred to as structural analysis [1]. The most important difference between social network analysis and the traditional or classic social research approach is that the contexts of the social actor, or the relationships between actors are the first consid- erations of the former, while the latter focuses on individual properties. A social network is a group of collaborating, and/or competing individuals or entities that are related to each other. It may be presented as a graph, or a multi-graph; each participant in the collaboration or competition is called an actor and depicted as a node in the graph theory. Valued relations between actors are depicted as links, or ties, either directed or undirected, between the corresponding nodes. Actors can be persons, organizations, or groups – any set of related entities. As such, SNA may be used on different levels, ranging from individuals, web pages, families, small groups, to large organizations, parties, and even to nations. According to the well known SNA researcher Lin Freeman [2], network analy- sis is based on the intuitive notion that these patterns are important features of the lives of the individuals or social entities who display them; Network analysts believe that how an individual lives, or social entity depends in large part on how that they are tied into the larger web of social connections/structures. Many believe, more- over, that the success or failure of societies and organizations often depends on the patterning of their internal structure. With a history of more than 70 years, SNA as an interdisciplinary technique de- veloped under many influences, which come from different fields such as sociology, mathematics and computer science, are becoming increasingly important across many disciplines, including sociology, economics, communication science, and psy- chology around the world. In the current chapter of this book, the author discusses M. Zhang () School of Journalism and Communication, Wuhan University, Wuhan, China e-mail: zhmxintop@yahoo.com.cn B. Furht (ed.), Handbook of Social Network Technologies and Applications, DOI 10.1007/978-1-4419-7142-5 1, © Springer Science+Business Media, LLC 2010 3
- 26. 4 M. Zhang the history of social network analysis, including its origin and development, in a brief manner, and discusses definition, features, fundamental concepts and research of social network analysis. In the end of this chapter, the author points out that devel- oping and looking for new techniques and tools that resolve corresponding problems challenging SNS research is urgent. 1.2 Social Network Analysis: Definition and Features Social network is formally defined as a set of social actors, or nodes, members that are connected by one or more types of relations [3]. Nodes, or network members, are the units that are connected by the relations whose patterns researchers study. The units are most commonly individuals, groups or organizations, but in princi- ple any units that can be connected to other units can be studied as nodes, such as web pages, blogs, emails, instant messages, families, journal articles, neighbor- hoods, classes, sectors within organizations, positions, or nations [4–6]. Research in a number of academic fields has shown that social networks operate on many levels, from families up to the level of nations, and play a critical role in determining the way problems are solved, organizations are run, and the degree to which individuals succeed in achieving their goals [7]. Traditionally, mainstream social research focus exclusively on the behavior of individuals. This approach neglects the social part or structure of human behavior; the part that is concerned with the ways individuals interact and the influence they have on one another [8]. However, social network analysts, take these parts as the primary building blocks of the social world, they not only collect unique types of data, they begin their analyses from a fundamentally different perspective than that had been not adopted by individualist or attribute-based social science. In social science, the structural approach, that is based on the study of interaction among social actors is called social network analysis [8]. The relationships that social network analysts study are usually those that link individual human beings, since these social scientists believe that besides individual characteristics, relational links or social structure, are necessary and indispensable to fully understand social phenomena. Specifically, Wetherell et al. describe social network analysis as follows [9, p. 645]: Most broadly, social network analysis (1) conceptualizes social structure as a network with ties connecting members and channelling resources, (2) focuses on the characteristics of ties rather than on the characteristics of the individual members, and (3) views communities as ‘personal communities’, that is, as networks of individual relations that people foster, maintain, and use in the course of their daily lives. Structural approach is not confined to the study of human social relationships. As Freeman pointed out [8], it is present in almost every field of science. For exam- ple, Freeman wrote that, molecular chemists examine how various kinds of atoms interact together to form different kinds of molecules, while electrical engineers
- 27. 1 Social Network Analysis: History, Concepts, and Research 5 observe how the interactions of various electronic components – like capacitors and resistors – influence the flow of current through a circuit. And biologists study the ways in which each of the species in an ecosystem interacts with and impinges on each of the others. There are different types of networks. Generally, network analysts differentiate the following networks: One Mode Versus Two Mode Networks. The former involve relations among a sin- gle set of similar actors, while the latter involve relations among two different sets of actors. An example of two mode network would be the analysis of a network con- sisting of private, for profit organizations and their links to non-profit agencies in a community [10]. Two mode networks are also used to investigate the relationship between a set of actors and a series of events. For example, although people may not have direct ties to each other, they may attend similar events or activities in a community and in doing so, this sets up opportunities for the formation of “weak ties” [11]. Complete/Whole Versus Ego Networks. Complete/whole or Socio-centric networks consist of the connections among members of a single, bounded community. Rela- tional ties among all of the teachers in a high school is an example of whole network. Ego/Ego-centric or personal networks are referred to as the ties directly connecting the focal actor, or ego to others, or ego’s alters in the network, plus ego’s views on the ties among his or her alters. If we asked a teacher to nominate the people he/she socializes with outside of school, and then asked that teacher to indicate who in that network socializes with the others nominated, it is a typical ego network. Social network analysis is the study of structure, because the social network ap- proach is grounded in the intuitive notion that the patterning of social ties in which actors are embedded has important consequences for those actors. This is the most important feature of SNA. Early structural intuitions is seen as come from sociol- ogists including Auguste Comte, Ferdinand Tönnies, Emile Durkheim, Sir Herbert Spencer. Freeman argued [8] that these early sociologists all tried to specify the different kinds of social ties that link individuals in different forms of social collec- tivities. Thus, since they were all concerned with social linkages, they all shared a structural perspective. If structural intuition is looked as the driving force of social network analysis, we could say that SNA is grounded in systematic empirical data, especially rela- tional, or network data. Relational data is different with the traditional, attribute, or sector data in that it used to describe and explain the relationship between two or more social actors (individuals i and j, for example), while attribute data describe and explain the relationship between two or more attributes of a single social ac- tor (individuals i or j, for example). Tables 1.1 and 1.2 show relational data and attribute data, respectively. In the context of relational data, as Table 1.1 shows, researcher explores the struc- ture of all the social actors (i.e., i1; j1; i2; j2 and other nodes), and the mathematical formula could be represented as Sij D f.ij/. However, when dealing with attribute data, researcher investigates correlation, causal, mediated, and other relationships
- 28. 6 M. Zhang Table 1.1 Relational data i1 j1 i2 j2 : : : i1 – Sj1i1 Si2i1 Sj2i1 Si1 j1 Si1j1 – Si2j1 Sj2j1 Sj1 i2 Si1i2 Sj1i2 – Sj2i2 Si2 j2 Si1j2 Sj1j2 Si2j2 – Sj2 : : : Si1 Sj1 Si2 Sj2 – Table 1.2 Attribute data Y x1 x1 x3 x4 : : : 1 : : : : : : : : : : : : : : : 2 : : : : : : : : : : : : : : : 3 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : N : : : : : : : : : : : : : : : between different variables (i.e., dependent and independent variables, Y and x1; x2; x3; x4 and other variables in Table 1.2). Y D f.x/ is mathematical formula in this context. The third prominent feature of SNA is it draws heavily on graphic imagery. In the field of SNA, researchers use points to represent social actors and lines to repre- sent linkages among them. There are two types of graphs: directed and undirected graphs. Directed graph consists of a set of nodes and a set of links (also called arcs or edges). A link e, is an ordered pair .i; j/ representing a connection from node i to node j. Node i is called the initial node of link e, i D init.e/, and node j is called the final node of the link: j D fin.e/. If the direction of a link is not important, or equivalently, if existence of a link between nodes i and j necessarily implies the existence of a link from j to i, we say that this network is an undirected graph. A path from node i to node j is a sequence of distinct links .i; u1/, .u1; u2/; : : :, .uk; j/. The length of this path is the number of links (here k C 1). An undirected graph can be represented by a symmetrical matrix M D .mij/, where mij is equal to 1 if there is an edge between nodes i and j, and mij is 0 if there is no direct link between nodes i and j. Table 1.3 shows an imaginary relational data matrix. There is a line connecting node A and node B. It is noticeable that this link is an ordered relation. Here A is the initial node of link, while B is the final node. Using directed graph to describe this data matrix, we will get Fig. 1.1. However, graph showed in Fig. 1.1 is rather primitive, because it only consists of six nodes and seven links. Figure 1.2 describes a more complex graph in a study of China inter-provincial interactions conducted by Jonathan Zhu [6]. In this con- text, there are 32 nodes (i.e., provinces) and numerous links between any pair of two nodes. There links describe information and population interactions in China mainland. It is clear that Beijing and Shanghai, the biggest cities in China, occupy the centric position in the graph.
- 29. 1 Social Network Analysis: History, Concepts, and Research 7 Table 1.3 An imaginary relational data matrix A B C D E F A – 1 1 0 0 0 B 0 – 1 1 0 0 C 1 1 – 0 0 0 D 0 0 0 – 1 1 E 0 0 0 0 – 1 F 0 0 0 1 1 – Fig. 1.1 Directed graph of relational data matrix in Table 1.3 Fig. 1.2 China inter-provincial interactions Figure 1.3 shows a more complex graph regarding the co-citation network in the research field of media economics [12]. In this graph, it is easy to know that the following documents, such as Picard 89, Albarran 96, Owen/Wildman 92, Scherer 73/90, Litman 79, Lacy 89,Bagdikian 83/00, and so on, occupy more
- 30. 8 M. Zhang Fig. 1.3 Co-citation network in the research field of media economics central positions in the network, indicating that they are more important than others. Reflected by the number of ties in the graph, we could see that there are more links point to them. Freeman argued [8] that unlike many other approaches to social research, net- work analysis has consistently drawn on various branches of mathematics both to clarify its concepts and to spell out their consequences in precise terms. Thus, the us- age of mathematical and/or computational models, is an important feature of SNA. This is the fourth feature of SNA. 1.3 The Development of Social Network Analysis: A Brief History As stated above, early sociologists in the late 1800s, including Émile Durkheim and Ferdinand Tönnies, are precursors of social network theory. Tönnies argued that so- cial groups can exist as personal and direct social ties that either link individuals who share values and belief or impersonal, formal, and instrumental social links.
- 31. 1 Social Network Analysis: History, Concepts, and Research 9 Durkheim gave a non-individualistic explanation of social facts arguing that social phenomena arise when interacting individuals constitute a reality that can no longer be accounted for in terms of the properties of individual actors. He distinguished be- tween a traditional society – “mechanical solidarity” – which prevails if individual differences are minimized, and the modern society – “organic solidarity” – that de- velops out of cooperation between differentiated individuals with independent roles [8]. Georg Simmel, writing at the turn of the twentieth century, was the first scholar to think directly in social network terms. His essays pointed to the nature of network size on interaction and to the likelihood of interaction in ramified, loosely–knit net- works rather than groups [13]. Social network as a relatively separate academic concept generated in 1920s– 1930s in the research filed of anthropology in Britain. Anthropologist Roger Brown was the first researcher who used the term social network, implying that social struc- ture is similar with a network and that interpersonal communication among individ- uals resembles relationship between a node and another nesting in the network [14]. One of the line of social network analysis could be traced back to Sociomery Method created by social psychologist Jacob Levy Moreno in 1930s, and this method paved the way for quantitative analysis in social network approach. In the 1930s, Moreno pioneered the systematic recording and analysis of social interaction in small groups, especially classrooms and work groups. According to Freeman [8], in Moreno’s 1934 book, he used the term “network” in the sense that it is used to- day. Freeman further pointed out that by 1938, then, the work of Moreno – with the help of Jennings and Lazarsfeld—had displayed all four of the features that define contemporary social network analysis [8]. The second line is a Harvard group led by W. Lloyd Warner and Elton Mayo, which exhibited research effort that focused on the study of social structure in the late 1920s. However, the Harvard effort never “took off” in Freeman’s eye, because it never provided a general model for a structural paradigm. As a matter of fact, the efforts at Harvard group are almost never recognized in historical reviews of social network analysis [8]. The 1940s–1960s is called by Freeman as the Dark Ages in the history of the development of SNA. In this period, there was no generally recognized approach to social research that embodied the structural paradigm. Social network analysis was still not identifiable either as a theoretical perspective or as an approach to data collection and analysis [8]. In the 1960s–1970s, a growing number of scholars worked to combine the different tracks and traditions. One large group was centered around Harrison White and his students at Harvard University: Ivan Chase, Bonnie Erickson, Harriet Friedmann, Mark Granovetter, Nancy Howell, Joel Levine, Nicholas Mullins, John Padgett, Michael Schwartz and Barry Wellman. Freeman called it as the Renaissance of SNA at Harvard. The Harvard school published so much important theory and research focused on social networks that social scientists everywhere, re- gardless of their field, could no longer ignore the idea. By the end of the 1970s, then, social network analysis came to be universally recognized among social scientists.
- 32. 10 M. Zhang According to Freeman’s statistics, Harrison White group at Harvard University was not the only ones who could lay claim to the social network approach. On the contrary, in the 40-year period from the late 1930s through the late 1970s, there were at least 17 research groups or centers adopted a general social network perspective. Of course, the developments at these groups or centers were not all independent of one another. Those that emerged later undoubtedly drew on the work of at least some of the earlier efforts [8]. Table 1.4 lists some founders and the most prominent researchers of SNA from 1940s through 1970s. However, it can’t provide more information regarding the internal structure of these founders and researchers, just like the traditional so- cial research could not discover the interaction patterns of social actors. Figure 1.4 describes the influences of parts of the above founders and researchers. When intro- ducing the basic concepts in the next part of this chapter, we will give more detailed explanations about this figure. Table 1.4 Noticeable research groups in the development of SNA: 1930s–1970s Time period Group leader Known researchers University/institution 1930s–1940s Kurt Lewin, John French, Alex Bavelas Dorwin Cartwright, Leon Festinger, Duncan Luce University of Iowa, MIT, University of Michigan Mid 1940s Charles P. Loomis Leo Katz, Charles Proctor, T. N. Bhargava Michigan State College Late 1940s Lévi–Strauss – University of Chicago Early 1950s Torsten Hägerstrand – Lund University Early 1950s Nicolas Rashevsky Walter Pitts, Herbert D. Landahl, Hyman G. Landau, Anatol Rapoport University of Chicago Mid 1950s Paul Lazarsfeld, Robert K. Merton James S. Coleman, Elihu Katz, Herbert Menzel, Peter Blau, Charles Kadushin Columbia University Mid 1950s Everett M. Rogers George Barnett, James Danowski, Richard Farace, Peter Monge, Nan Lin, William Richards, Ronald Rice Iowa State University, Michigan State University Mid 1950s Alfred Reginald Radcliffe–Brown, Max Gluckman John Barnes, John Barnes, J.Clyde Mitchell, Elizabeth Bott, Sigfried Nadel Manchester University, London School of Economics Late 1950s Karl Wolfgang Deutsch, Ithiel de Sola Pool Fred Kochen MIT Late 1950s Linton C. Freeman, Morris H. Sunshine Thomas Fararo, Sue Freeman Syracuse University Early 1960s Claude Flament – Paris Sorbonne University (continued)
- 33. 1 Social Network Analysis: History, Concepts, and Research 11 Table 1.4 (continued) Time period Group leader Known researchers University/institution Mid 1960s Edward O. Laumann Stephen Berkowitz, Ronald Burt, Joseph Galaskiewicz, Alden Klovdahl, David Knoke, Peter Marsden, Martina Morris, David Prensky, Philip Schumm University of Michigan Late 1960s Peter Blau, James A. Davis – University of Chicago Late 1960s Robert Mokken Jac Anthonisse, Frans Stokman 1960s–1970s Harrison Colyer White Peter Bearman, Paul Bernard, Phillip Bonacich, Ronald L. Breiger, Kathleen M. Carley, Ivan Chase, Bonnie Erickson, Claude S. Fischer, Mark Granovetter, Joel Levine, Siegwart M. Lindenberg, Barry Wellman, Christopher Winship Harvard University When the concept of social network has been recognized by more and more researchers, more contributions have been made in research methodology: more and more measurement, data collection and analysis technologies were created and developed to understand social construe and relationships better, and these in turn advanced social network research. In the 1980s, a number of sociologists began to use SNA as analytical technique to examine social and economic phenomena. In mid 1980s, Mark Granovetter, pro- posed the concept of “embedded-ness”, guiding SNA approach into the mainstream social research field again. Granovetter argued that the operation of economics is embedded in social structure, however, the core social structure is individuals’ so- cial networks. In early 1980s, Granovetter formulated marketing network theory in his well known article “Where Do Markets Come From?” [15]. After 1990s, SNA has been gradually associated with social capital, drawing scholars’ attention from the field of sociology, politics, economics, communication science, and other disciplines. Ronald Burt’s book Structural Holes is representa- tive work of this period. Burt argues that social capital has not relationship with the strength of ties, but with the existence of structural holes. Lin Nan, another well known sociologist who proposed Social-resource theory, studied SNA from the so- cial capital perspective. In the next part of this chapter, when comes to theorization of SNA research design, the author will discuss Burt and Lin more.
- 34. 12 M. Zhang Fig. 1.4 Influences on some founders of SNA [8, p.131] 1.4 Basic Concepts of Social Network Analysis Social network is formally referred to as a set of social actors, or nodes, members that are connected by one or more types of relations. To understand networks and their participants, researchers should evaluate the location of actors in the network. To measuring location of each node, one should use the concept centrality and other related concepts. Through empirical measurement of a network, one will find var- ious roles and groupings in a network – who are the connectors, mavens, leaders, bridges, isolates? where are the clusters and who is in them? who is in the core of the network? And, who is on the periphery? In the following of this part, important concepts, such as ties, density, centrality, cliques and other concepts will be explained. 1.4.1 Ties Ties or links connect two and more nodes in a graph. Many human behaviors, such as advice seeking, information-sharing, and lending money to somebody are directed ties while co-memberships are examples of undirected ties. Directed ties may be reciprocated, as would be the case for two people who visit one another, or they may exist in only one direction as when only one gives emotional support to
- 35. 1 Social Network Analysis: History, Concepts, and Research 13 the other [16]. Both directed and undirected ties can be measured as binary ties that either exist or do not exist within each dyad, or as valued ties that can be stronger or weaker, transmit more or fewer resources, or have more or less frequent contact. 1.4.2 Density One of the most widely used, and perhaps over-used, concepts in graph theory is that of “density”, which describes the general level of linkage among the points in a graph. A “complete” graph is one in which all the points are adjacent to one another: each point is connected directly to every other point. As an attempt to summarize the overall distribution of lines, the concept of density aims to measure how far from this state of completion the graph is [14]. The density of a graph is quantitatively defined as the number of links divided by the number of vertices in a complete graph with the same number of nodes. It is an indicator for the general level of connectedness of the graph. Density is one of the most basic measures in network analysis and one of the most commonly used notions in social epidemiology. Some network structures are par- ticularly advantageous for certain functions [17]. For example, dense networks are particularly good for coordination of activity among the actors (because everyone knows everyone’s business). In the case of Fig. 1.1, results of density measures(ego networks) are shown in Table 1.5. 1.4.3 Path, Length, and Distance Nodes or actors may be directly connected by a line, or they may be indirectly connected through a sequence of lines. A sequence of lines in a graph is a “walk”, and a walk in which each point and each line are distinct is called a path. The concept of the path is, after those of the node and the line, one of the most basic of all graph theoretical concepts. The length of a path is measured by the number of lines which make it up. The distance between two nodes is the length of the shortest path (the “geodesic”) which connects them [14]. Table 1.5 Density measures of Fig. 1.1 Size Ties Pairs Density A 2:00 2:00 2:00 100:00 B 3:00 2:00 6:00 33:33 C 2:00 1:00 2:00 50:00 D 3:00 2:00 6:00 33:33 E 2:00 2:00 2:00 100:00 F 2:00 1:00 2:00 50:00
- 36. 14 M. Zhang Table 1.6 Geodesic distances of nodes in Fig. 1.1 A B C D E F A 0 1 1 2 3 2 B 2 0 1 1 2 2 C 1 1 0 2 3 3 D – – – 0 1 1 E – – – 2 0 1 F – – – 1 1 0 As to graph in Fig. 1.1, the average distance (among reachable pairs) is 1.667, distance-based cohesion(“compactness”) is 0.511 (range 0–1; larger values indicate greater cohesiveness), distance–weighted fragmentation (“breadth”) is 0.489. As to every node in Fig. 1.1, the Geodesic Distances are shown in Table 1.6. 1.4.4 Centrality The measures of centrality identify the most prominent actors, especially the star or the “key” players, that is, those who are extensively involved in relationships with other network members. The most important centrality measures are: degree centrality, closeness centrality and between-ness centrality. (1) Degree Centrality. Degree of a node is the number of direct connections a node has. Degree centrality is the sum of all other actors who are directly connected to ego. It signifies activity or popularity. Lots of ties coming in and lots of ties coming out of an actor would increase degree centrality. (2) Between-ness Centrality. This type of centrality is the number of times a node connects pairs of other nodes, who otherwise would not be able to reach one another. It is a measure of the potential for control as an actor who is high in “between-ness” is able to act as a gatekeeper controlling the flow of re- sources (information, money, power, e.g.) between the alters that he or she connects. This measurement of centrality is purely structural measure of popu- larity, efficiency, and power in a network; in other words, the more connected or centralized actor is more popular, efficient, or powerful. (3) Closeness Centrality. Closeness centrality is based on the notion of distance. If an node or actor is close to all others in the network, a distance of no more than one, then it is not dependent on any other to reach everyone in the network. Closeness measures independence or efficiency. With disconnected networks, closeness centrality must be calculated for each component. Table 1.7 indicated centrality measures of Fig. 1.1. As to complete network, when measuring with Degree Centrality, network centralizations are both 4.000% for in-degree and out-degree measures (asymmetric model); when using Freeman Between-ness Centrality indicator, un-normalized centralization of the complete
- 37. 1 Social Network Analysis: History, Concepts, and Research 15 Table 1.7 Centrality measures of Fig. 1.1 Out-degree In-degree In-closeness Out-closeness Between-ness A 2 1 1.500 3.167 0 B 2 2 2.000 3.500 6 C 2 2 2.000 3.167 1 D 2 2 3.500 2.000 6 E 1 2 3.167 1.500 0 F 2 2 3.167 2.000 1 Table 1.8 Two cliques of graph in Fig. 1.1 Sub-group 1 Sub-group 2 A 1.000 0.000 B 1.000 0.333 C 1.000 0.000 D 0.333 1.000 E 0.000 1.000 F 0.000 1.000 network is 22.00%; when using Closeness Centrality Measures (method: Recipro- cal Geodesic Distances), the results are both 51.00% for network in-centralization and out-centralization. 1.4.5 Clique A clique in a graph is a sub-graph in which any node is directly connected to any other node of the sub-graph. There two cliques in the graph of Fig. 1.1, that is, subgroup fA, B, Cg and fD, E, Fg. Clique proximities analysis shows the probability of clique members that each node is adjacent to, as described in Table 1.8. 1.5 Research of SNA: Design, Theorization, and Data Processing 1.5.1 Designing a Social Network Analysis Before conducting a SNA study, especially before collecting network data, one must first decide what kinds of networks and what kinds of relations they will study. As stated above, there have two important dimensions along which network data vary: one-mode vs. two-mode networks and complete vs. ego networks. As a general rule, researchers must make these choices at the beginning of study. Complete/whole networks, taking a bird’s eye view of the social structure, focus on all social actors rather than privileging the network surrounding any particular
- 38. 16 M. Zhang actor. These networks begin from a list of included actors and include data on the presence or absence of relations between every pair of actors. When examining all students and their interpersonal relationship in a class [18], or a network of actors appearing on film or television showing who has co-starred with whom [5], a whole network approach should be applied. Generally, researchers using whole network data frequently analyze more than one relation. When researcher adopts the whole network perspective, he/she will inquire each social actor and all other individu- als to collect relational data, then transforming into matrix (i.e., network data). In this situation, emphasis on data analysis is not the nature of each relation type, but structure of relation. Ego-centric network data, however, focus on the network surrounding one node, or in other words, the single social actor. Data are on nodes that share the chosen relation(s) with the ego and on relations between those nodes. Ego network data can be extracted from whole network data by choosing a focal node and examining only nodes connected to this ego. Ego network data, like whole network data, can also include multiple relations. These relations can be collapsed into single networks, as when ties to people who provide companionship and emotional aid are collapsed into a single support network [19]. Unlike whole network analyses, which com- monly focus on one or a small number of networks, ego network analyses typically sample large numbers of egos and their networks. Researchers using ego network approach emphasize the significance of individual’s exploitation of his/her social network for social resources. In these researchers’ view, individual’s social network influences his/her social attitude and behavior. When studying whole networks, researchers most frequently collect data on a single type of node in networks where every node could conceivably be connected to any other nodes. Most of the networks they analyze are one-mode networks. Two- mode networks, involve relations among two different sets of actors or nodes – typically organizations and organization members, or events and attendees. In these two-mode networks or affiliation networks, relations consist of things such as mem- berships or attendance at events that cannot exist between nodes of the same type: A person can attend an event or belong to an organization, but a person cannot attend or belong to another event or organization [20]. After deciding what kinds of networks and what kinds of relations under consid- eration, researchers should decide to how to collect network data. Many methods could be used, including (trace) observation, archives and historical materials anal- ysis, survey, interview, and experiment [21,22]. When using survey to collect data, the following techniques could be consid- ered in designing questionnaire. (1) Name generators: researchers ask respondents to list the people with whom they share ties, and further ask the types, strength or importance, and other characteristics of these ties. This technique is especially suitable for ego network data. (2) Structurally selecting format: respondents are asked to indicate the people with whom they have relations, however, the number of the people should not larger than a threshold. For example, a probable ques- tion may ask respondents that: In recently 6 months, whom do you interact with (you can list five persons at the most)? (3) Indicating characteristics of network
- 39. 1 Social Network Analysis: History, Concepts, and Research 17 members: researchers may ask respondents report democratic, societal, attitudinal, and behavioral properties of their network members. (4) Position generators, which was put forward by Lin Nan and colleagues, ask respondents to list their network members in different social ranks. Interview as an often used method, also helps SNA researchers to collect ego network data. Researchers could ask respondents’ circle of friends, peer relations, and primitive comradeship. This data collection method is also used to study social support network. 1.5.2 Theorization in Social Network Analysis Theorization is the basic goal of all research fields of social science. As a perspective or a research paradigm, social network analysis takes as its starting point the premise that social life is created primarily and most importantly by relations and the patterns they form, and it provides a way of looking at a problem, but it does not predict what we will see [20]. However, in the stage of research design, scholars should do their best to carry out research with the application of related theories, and aim to extend and modify social theories. In fact, several famous theories have been exactly developed under the social network perspective. Diffusion of innovations theory, DIT, explores social networks and their role in influencing the spread of new ideas, products, and practices, etc. As Rogers’ s book shows, many communication theories, such as the theory of two step flow of communication, heterophily and communication channels, have been integrated in related studies. Taking communication science as an example, in recent years, many research articles examining the impacts of communication networks on the adop- tion and usage of new information and communication technologies (ICTs) among specific social groups in different cultural contexts [23–25] have been published in top international journals, such as Information Research, Communication Research, Journal of Computer Mediated Communication, etc. Using a network perspective, Mark Granovetter [11] put forward the theory of the “strength-of-weak-ties”. Granovetter found in one study that more numerous weak ties can be important in seeking information and innovation. Because cliques have a tendency to have more homogeneous opinions and common traits, individuals in the same cliques would also know more or less what the other members know. To gain new information and opinion, people often look beyond the clique to their other friends and acquaintances. However, Bian Yanjie, a Chinese social scientist, found that in China, personal networks (Guanxi1 ) are used to influence authorities who in 1 Guanxi, used to describe a personal connection between two people in which one is able to prevail upon another to perform a favor or service, or be prevailed upon, is a central concept in Chinese society.
- 40. 18 M. Zhang turn assign jobs as favors to their contacts, which is a type of unauthorized activity facilitated by strong ties characterized by trust and obligation. Bian called his theory as Strong Ties [26]. The Small World is other example of theorization of social network research. The idea of small world hypotheses that in a network, most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps. This concept gave rise to the famous phrase “Six Degrees of Sepa- ration”. In psychologist Stanley Milgram’s experiment, a sample of US individuals were asked to reach a particular target person by passing a message along a chain of acquaintances. Result shows that the average length of successful chains turned out to be about five intermediaries or six separation steps. After 1990s, scholars extend the theorization of social network analysis greatly, among which the most famous were Ronald Burt’s theory of Structural Holes and Lin Nan’s Social Capital Theory. Burt argue that the weaker connections between groups are holes in the social structure of the market. These holes in social structure create a competitive advantage for an individual whose relationships span the holes. Finally, structural holes are an opportunity to broker the flow of information between people, and control the projects that bring together people from opposite sides of the hole. As one of the very first scholars to undertake serious research on the social networks foundation of social capital, Lin Nan’s studies in recent years produce uni- versal influences around the world. Lin’s assumption is that the macro-level social structure is a type of hierarchical structure, which is determined by the allocation of various resources such as wealth, social status, and power [27,28]. In his famous book Social Capital: A Theory of Social Structure and Action, Lin explains the im- portance of using social connections and social relations in achieving goals. Social capital as resources, accessed through such connections and relations, is critical in achieving goals for individuals, social groups, organizations, and communities. The framework of Lin’s social capital research consists of the following elements: social actor’s network position, the strength of ties, resources, redound, and otherwise. 1.5.3 SNA Data Processing Tools As stated above, since network data are different with the traditional attribute data, social network analysts use corresponding techniques to process data collected. Social network analysis software is used to identify, represent, analyze, visualize, or simulate nodes and ties from various types of input data. At the present, popular social network tools are UCINET, PAJEK, STRUC- TURE, NETMINER, STOCNET, and others. UCINET is developed by Steve Borgatti, Martin Everett and Lin Freeman [29]. The program is distributed by Analytic Technologies. It works in tandem with freeware program called NETDRAW for visualizing networks, which is installed automatically with UCINET. This type of software can process, read and write
- 41. 1 Social Network Analysis: History, Concepts, and Research 19 a multitude of differently formatted text files, as well as Excel files, and handle a maximum of 32,767 nodes (with some exceptions), although practically speaking, many procedures get too slow around 5,000–10,000 nodes. Centrality measures, subgroup identification, role analysis, elementary graph theory, permutation-based statistical analysis, and other SNA measures can be performed on the software. PAJEK, Slovene word for Spider, is an open source Windows program for analysis and visualization of large networks having some thousands or even mil- lions of vertices. It started development in November 1996, and is implemented in Delphi (Pascal). It is freely available, for noncommercial use, at its homepage: http://vlado.fmf.uni-lj.si/pub/networks/pajek/.The main goals in the design of Pajek are to support abstraction by (recursive) factorization of a large network into several smaller, which can be treated further using more sophisticated methods; to provide the user with some powerful visualization tools; and to implement a selection of efficient algorithms for analysis of large networks. The program STRUCTURE is a free software package for using multi-locus genotype data to investigate population structure. Its uses include inferring the pres- ence of distinct populations, assigning individuals to populations, studying hybrid zones, identifying migrants and admixed individuals, and estimating population al- lele frequencies in situations where many individuals are migrants or admixed. It can be applied to most of the commonly-used genetic markers, including SNPs, mi- crosatellites, RFLPs and AFLPs. Furthermore, functions that STRUCTURE provide cannot be found in other social network data processing tools. NETMINER is an innovative software tool for Exploratory Analysis and Visual- ization of Network Data. It can be used for general research and teaching in social networks. This tool allows researchers to explore their network data visually and interactively, helps them to detect underlying patterns and structures of the network. Especially, it can be effectively applied to various business fields where network- structural factors have great deal of influences on the performance (e.g., intra and inter-organizationalfinancial Web criminal/intelligence informetric telecommunica- tion distribution transportation networks). Statistically, this program supports many standardized computer methods, including descriptive statistics, ANOVA, correla- tion, and regression. 1.6 Summary Social network analysis is the study of social structure. The social network analysts are interested in how the individual is embedded within a structure and how the structure emerges from the micro-relations between individual parts [30]. Hence, the greatest advantage of SNA is that it considers how the communication net- work structure of a group shapes individuals’ cognition, attitude and behavior. As an approach to social research, SNA displays four features: structural intuition, sys- tematic relational data, graphic images and mathematical or computational models [8]. In its more than 70 years of history, social network analysts have developed
- 42. 20 M. Zhang a number of formal and precise ways of defining terms like “relation”, “density”, “centrality”, “clique” and others, so that they can be applied unambiguously to data on populations of individuals. Recognizing that “we all connect, like a net we cannot see” [31], social net- work analysis is more and more popular with researchers from various fields such as sociology, mathematics, computer science, economics, communication science, and psychology around the world. In social sciences, theorization of SNA has been improved obviously in the recent two decades, although it had been criticized be- fore 1980s. However, as new information and communication technologies (e.g., the Internet, mobile phones, digital broadcast, etc.) have made the collection of social network data much easier on a much larger scale at a much lower cost than what con- ventional methods could offer, problems regarding the analysis and the subsequent interpretation of the resulting data raise. Existing techniques seem to be inadequate to handle new types of social network data that are continuous, dynamic, and multi- level [6]. Thanks to the current situation, developing and looking for new techniques and tools that resolve these problems should become social and engineering scien- tists research agenda. References 1. B. Wellman and S. D. Berkowitz (Eds). “Social Structures: A Network Approach.” Cambridge: Cambridge University Press, 1988. 2. L. C. Freeman. “What is Social Network Analysis?” Last Update Friday, 08-Feb-2008, Avail- able at: http://www.insna.org/sna/what.html 3. S. Wasserman and K. Faust. “Social Network Analysis: Methods and Applications.” Cambridge: Cambridge University Press, 1994. 4. S. A. Boorman and H. C. White. “Social Structure from Multiple Networks. II. Role Struc- tures.” American Journal of Sociology, Vol. 81, No. 6, 1976, pp. 1384–1446. 5. D. J. Watts. “Networks, Dynamics, and the Small-World Phenomenon.” American Journal of Sociology, Vol. 105, No. 2, 1999, pp. 493–527. 6. J. J. H. Zhu. “Opportunities and Challenges for Network Analysis of Social and Behavioral Data.” Seminar Series on Chaos, Control and Complex Networks City University of Hong Kong, Poly U University of Hong Kong IEEE Hong Kong RA/CS Joint Chapter, 2007. 7. H. D. White, B. Wellman, and N. Nazer. “Does Citation Reflect Social Structure? Longitudi- nal Evidence from the ‘Globenet’ Interdisciplinary Research Group.” Journal of the American Society for Information Science and Technology, Vol. 55, No. 2, 2004, pp. 111–126. 8. L. C. Freeman. “The Development of Social Network Analysis: A Study in The Sociology of Science.” Canada: Empirical Press Vancouver, 2004. 9. C. Wetherell, A. Plakans, and B. Wellman. “Social Networks, Kinship, and Community in Eastern Europe.” Journal of Interdisciplinary History, Vol. 24, No. 1, 1994, pp. 639–663. 10. P. Hawe, C. Webster, and A. Shiell. “A Glossary of Terms for Navigating the Field of So- cial Network Analysis.” Journal of Epidemiology and Community Health, Vol. 58, 2004, pp. 971–975. 11. M. Granovetter. “The Strength of Weak Ties.” American Journal of Sociology, Vol. 78, 1973, pp. 1360–1380. 12. M. X. Zhang. “Co-citation Network and the Structure of Paradigms in the Research Field of Media Economics: 1999–2008.” Unpublished manuscript, 2011. 13. G. Simmel. “On Individuality and Social Forms.” Chicago: University of Chicago Press, 1908/1971.
- 43. 1 Social Network Analysis: History, Concepts, and Research 21 14. J. Scott. “Social Network Analysis: A Handbook.” London: Sage Publications, 1987. 15. M. Granovetter. “Economic Action and Social Structure: The Problem of Embedded-ness.” American Journal of Sociology, Vol. 91, No. 3, 1985, pp. 481–493. 16. G. Plickert, R. Côté, and B. Wellman. “It’s Not Who You Know. It’s How You Know Them: Who Exchanges What with Whom?” Social Networks, Vol. 29, No. 3, 2007, pp. 405–429. 17. J. Liu. “An Introduction to Social Network Analysis (In Chinese).” Beijing: Social Sciences Academic Press, 2004. 18. M. X. Zhang. “Exploring Adolescent Peer Relationships Online and Offline: An Empirical and Social Network Analysis.” Proceedings of 2009 WRI International Conference on Communi- cations and Mobile Computing, Vol. 3, 2009, pp. 268–272. 19. B. Wellman. “The Community Question: The Intimate Networks of East Yorkers.” American Journal of Sociology, Vol. 84, 1979, pp. 1201–1231. 20. A. Marin and B. Wellman. “Social Network Analysis: An Introduction.” In: P. Carrington and J. Scott (Eds). Handbook of Social Network Analysis. London: Sage, 2010. 21. D. Gibson. “Concurrency and Commitment: Network Scheduling and Its Consequences for Diffusion.” Journal of Mathematical Sociology, Vol. 29, No. 4, 2005, pp. 295–323. 22. R. Gould. “Insurgent Identities: Class, Community and Protest in Paris from 1848 to the Commune.” Chicago: University of Chicago Press, 1995. 23. L. Wei and M. X. Zhang. “The Adoption and Use of Mobile Phone in Rural China: A Case Study of Hubei, China.” Telematics and Informatics, Vol. 25, No. 3, 2008, pp. 169–186. 24. L. Wei and M. X. Zhang. “The Impacts of Internet Knowledge on College Students’ Intention to Continue to Use the Internet.” Information Research, Vol. 13, No. 3, 2008, paper 348. Available at http://InformationR.net/ir/13–3/paper348.html 25. J. J. H. Zhu and Z. He. “Perceived Characteristics, Perceived Needs, and Perceived Popularity: Adoption and Use of the Internet in China.” Communication Research, Vol. 29, No. 4, 2002, pp. 466–495. 26. Y. J. Bian. “Bringing Strong Ties Back in: Indirect Ties, Network Bridges, and Job Searches in China.” American Sociological Review, Vol. 62, No. 3, 1997, pp. 366–385. 27. N. Lin, K. Cook, and R. Burt (Eds). “Social Capital: Theory and Research.” New Brunswick, NJ: Transaction Press, 2001. 28. N. Lin. “Social Capital: A Theory of Social Structure and Action.” NewYork: Cambridge University Press, 2001. 29. S. Borgatti, M. Everett, and L. Freeman. “Ucinet for Windows: Software for Social Network Analysis.” Harvard, MA: Analytic Technologies, 2002. 30. R. Hanneman. “Introduction to Social Network Methods.” 2002, Available at: www.faculty. ucr.edu/,hanneman/ 31. R. Mickenberg and J. Dugan. “Taxi Driver Wisdom.” San Francisco: Chronicle, 1995.
- 44. Chapter 2 Structure and Dynamics of Social Networks Revealed by Data Analysis of Actual Communication Services Masaki Aida and Hideyuki Koto 2.1 Introduction Up to now, data of actual communication services obtained from communication networks, such as the volume of traffic and the number of users, has mainly been used to forecast traffic demands and provision network facilities. It can be said that this use focuses on the “quantitative” side of the data. On the other hand, such data can also illuminate several characteristics of the structures of the human society. This chapter introduces a new “qualitative” use of communication network data. We try to extract social information from the data, and investigate the universal structure of social networks that underlie the most popular communication services. Our expectation is that each communication service provides a different window on the universal social network structure. The question is how to access those windows. A direct technique for examining social network structures is the questionnaire approach. However, its extremely high cost makes it impractical if we target a comprehensive analysis of the universal social network structure. Our solution is to collect and analyze the quantitative data generated by communication services. The contents of communication logs etc. offer views of the individual situations associated with that service. Examples of these situations include interpersonal relationships in an organization and agreements reached between corporations. However, conventional analysis fails to extract complete images of the universal social network structure. In this chapter, we focus on the power laws that appear in the data of actual communication services. In explaining the reasons that underlie the power laws, we elucidate the whole universal social network structure. Since the power laws exam- ined in this chapter describe the relations present in coarse data, detailed behaviors (e.g., who is communicating with who) of each user cannot be observed. However, we can expect to extract a more nearly universal structure that is independent of the superficial structures present in each data set. Once we develop a universal model of M. Aida () Tokyo Metropolitan University, Hino-shi, Tokyo 191-0065, Japan e-mail: maida@sd.tmu.ac.jp B. Furht (ed.), Handbook of Social Network Technologies and Applications, DOI 10.1007/978-1-4419-7142-5 2, © Springer Science+Business Media, LLC 2010 23
- 45. 24 M. Aida and H. Koto social networks, we can better understand the process of service penetration and can find a better activation method that can replace the word-of-mouth communication- based marketing approach, for not only existing services but also future services. In addition, a comprehensive understanding of the universal social network struc- ture could be applied to not only communication services but also more general commodities and services such as business and marketing strategies. We explain here why we focus on power laws. We know that certain types of dis- tributions (e.g., normal, Poisson, etc.) originate from randomness. Differing from these distributions, power laws can be assumed to have deterministic causes. There- fore, investigation of the reason of power laws is not disturbed by randomized effect, and the cause of power laws is connected to other phenomena. Our approach is summarized as follows. We analyze three different data sets: the volume of traffic in the initial stage of NTT DoCoMo’s i-mode service [3], the logs of NTT DoCoMo’s voice traffic, and the number of mixi users [9]. Hereafter, we call these data sets as Service I, II, and III, respectively. Service I is the first Internet access service offered over cellular phone terminals, Service II is a cellular phone service, and Service III is the largest social networking service (SNS) in Japan. By combin- ing these analyses we obtain three results with regard to the social networks that underlie specific communication services. The first is the degree distribution of so- cial networks, the second is the topological rules of social networks, and the last is user dynamics with regard to the actions needed to join a communication service. The first result was verified through a cross-check using different data; the logs of voice traffic presented by KDDI’s cellular phone service [11]. We call this data set as Service IV. The rest of this chapter is organized as follows: Section 2.2 provides a conceptual image of the methods available for analyzing social networks. Section 2.3 analyzes, according to [1, 2], the data of the cellular phone service (Service I and II) to de- rive partial information on the social network structure. The partial information so obtained cannot completely determine the model of social networks and there is an undetermined parameter in the model. Section 2.4 analyzes data on SNS (Service III) users to supplement the partial information obtained in Sect. 2.3. The combined use of both results enables us to determine the value of the parameter in the social net- work model. The result is a social network model that is self-consistent with the data observed from different services (Service I, II, and III). In Sect. 2.5, we verify the validity of our social network model by using the traffic logs of a cellular phone service that were not analyzed in earlier sections (Service IV). Section 2.6 concludes our discussion with a brief summary. 2.2 Analysis Strategy We use graph G.V; E/ to represent the relationship of people exchanging infor- mation, where V is a set of nodes (people) and E is a set of links (information exchanges) between nodes. We call G.V; E/ the social network.
- 46. 2 Structure and Dynamics of Social Networks Revealed 25 universal social networks behind communication services social network structures observed from service 1 social network structures observed from service 2 social network structures observed from service 3 Fig. 2.1 The relationship between the universal social network and images obtained from specific communication services The global structure of G.V; E/ cannot, unfortunately, be observed directly although the object of our interest is to clarify the structure of G.V; E/. Our so- lution is to adopt the approach of investigating the structure of G.V; E/ indirectly; we analyze specific communication services, such as cellular phone and SNS. Our purpose is not to investigate the specific services themselves, but to use them to elucidate the structure of social network G.V; E/. How then is it possible to extract the universal social network structure? The con- cept of our approach is illustrated in Fig. 2.1. The network at the center of Fig. 2.1 is the “multi-dimensional” social network, and the three eyes represent three dif- ferent services that hold partial information of the social network as “contracted” information. Although the “universal” social network at the center of the figure cannot be observed directly, we assume that sets of partial information can be ex- tracted from specific communication services. These partial information sets may allow us to construct the “multi-dimensional” or “universal” social network model by combining them. 2.3 Analysis of Social Networks Based on Traffic Data of Internet Access Service Offered Over Cellular Phones In this section, we introduce the partial information set created by analyzing the data of the cellular phone service.
- 47. 26 M. Aida and H. Koto 2.3.1 Data To Be Analyzed This subsection analyzes the data that holds the relationship between the number of users and email traffic during the early growth period of Service I; the world’s first Internet access service from cellular phone terminals [3]. Since Service I was launched on February 22, 1999, the service has seen an explosive increase in the number of users. In the first one and half years (up to August 2000) the number of users exceeded ten million. The process by which a network service can acquire users at such a dramatic rate offers an interesting window on the structure of social networks and user behavior regarding hot-selling products. This set of Service I data is useful for understanding social networks because it has the following properties: Since the number of Service I users increased explosively within a short period, it can be assumed that the Service I traffic was little affected by external factors such as a change in people’s lifestyle. Since most cellular phones are exclusively used by their owners, traffic between cellular phones can be regarded as information exchange between people. Since most Service I emails are one-to-one communication, it can be assumed that email traffic is closely related to the number of pairs of Service I users who are exchanging information with each other. Since the cost of sending an email is far lower than that of talking on the phone, it can be assumed that the volume of email communication is little affected by such external factors as the income level of the individual users. Since the early period of the Service I had few problems with unwanted advertis- ing emails sent to users indiscriminately, it can be assumed that almost all traffic arose from existing social networks. During the early expansion period, 6 months from the beginning of August 1999 to the end of January 2000, the number of Service I users increased almost threefold, from 1,290,000 to 3,740,000. The relationship between the Web traffic (number of Web access attempts) and the number of Service I users during this period can be modeled as: (Web traffic) / n; (2.1) where n is the number of users (chart on the left in Fig. 2.2). This is self-evident as long as the average number of Web access attempts per user is constant. Con- versely, the fact that the above relation holds means that people’s average usage of the Service I service did not change during this period. In other words, there is no evidence that the earliest subscribers to the Service I were heavier users. Meanwhile, the volume of email traffic (number of email messages) can be modeled as: (Email traffic) / n5=3 : (2.2) Thus, a power law applies (chart on the right of Fig. 2.2). If the volume of commu- nication per user remained constant even as n increased, then the volume of email traffic should be proportional to n. The fact that email traffic is proportional to n1C˛
- 48. 2 Structure and Dynamics of Social Networks Revealed 27 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Line of gradient = 1 Logarithm of Web traffic Logarithm of the number of i-mode users Service I Web traffic 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Logarithm of email traffic Logarithm of the number of i-mode users Line of gradient = 1 Line of gradient = 2 Service I email traffic Fig. 2.2 The relationship between the number of users and the volume of Service I traffic for Web and email .˛ ' 2=3/ suggests that an increase in n results in an increase in the number of Service I users a single user communicates with. Therefore, ˛ ' 2=3 characterizes the rate of increase in email traffic. This also tells us something about the strength of human relations in social networks. The following examines the graphical structure of universal social networks G.V; E/, involving not only Service I users but also others, using the power law (2.2) identified from the email traffic data described above. 2.3.2 Definition of Symbols and Problem Description As mentioned in Sect. 2.2, G.V; E/ represents the social network, and the number of people in V is N (jV j D N ). We assume that G.V; E/ does not change over time. We use a rule to select n nodes from V ; the subset of these selected nodes is Vi.n/ .n N /. Let Gi.Vi.n/; Ei.n// be the subgraph induced by Vi.n/ from G.V; E/. That is, a node pair is connected by a link in Gi.Vi.n/; Ei.n// if and only if the corresponding node pair in G.V; E/ is connected by a link. Each element of Vi.n/ is an Service I customer and social networks among all Service I customers are represented by Gi.Vi.n/; Ei.n// (see Fig. 2.3). Equation (2.1) indicates that the usage of Service I by individual users did not change even as the number of Service I users increased. Therefore, it can be assumed that the traffic per link between a user and a Web site remained constant. Similarly, we assume that the average email traffic per link is also constant irrespective of the number of Service I users.1 Thus, the number of links jEi.n/j becomes, jEi.n/j D O.n1C˛ /: (2.3) 1 The fact that traffic per link is not affected by the number of Service I users, n, has been indirectly confirmed from Service II. See Appendix A for details.
- 49. 28 M. Aida and H. Koto Graph expressing relationships between humans (potential customers) Induced subgraph derived to depict the relationships between i-mode users Users subscribing to the i-mode service Users not subscribing to the i-mode service Fig. 2.3 Example of G.V; E/, a graph showing the structure of the social networks, and Gi.Vi.n/; Ei.n//, the subgraph induced from Service I users The issue addressed by this paper is not the study of Gi.Vi.n/; Ei.n//, or social networks established between Service I users, but G.V; E/, or universal so- cial networks among both users and non-users of the Service I, as indicated by the traffic data of Service I. Figure 2.3 shows the relation between G.V; E/ and Gi.Vi.n/; Ei.n//. The upper graph, G.V; E/, shows universal social networks while the bottom graph is a subgraph, Gi.Vi.n/; Ei.n//, derived from G.V; E/, showing the social networks among Service I users. The number of Service I users and the volume of email traffic correspond to the number of nodes and the number of links, as derived in (2.3), in Gi.Vi.n/; Ei.n//. The structure of G.V; E/ and how people begin to subscribe to the Service I are considered below. 2.3.3 How People Subscribed to the Service I and the Structure of Social Networks First, we introduce two different schemes for numbering the elements of V , and define three sequences of node degree (the number of links that a node has) based on the numbering. We call the node with the largest node degree as node 1. Similarly, we call the node with the jth largest node degree as node j. In addition, let the magnitude of node degree of node j be D.j/. Next, we introduce another numbering of elements in V according to the time of subscribing to the Service I. Let Di.`/ be the node degree of the `th earliest subscribed node in G.V; E/. Similarly, let di.n; `/ be the degree of the `th earliest subscribed node with respect to Gi.Vi.n/; Ei.n// when the number of Service I users is n.
- 50. 2 Structure and Dynamics of Social Networks Revealed 29 Fig. 2.4 Example of ci.n/ Users not subscribing to the i-mode service Users subscribing to the i-mode service the number of i-mode users: Assume that the degree of Service I user in Gi.Vi.n/; Ei.n// can be related to his or her degree in G.V; E/ as follows: n X `D1 di.n; `/ D ci.n/ n X `D1 Di.`/; (2.4) where ci.n/ indicates the ratio of the number of Service I user’s acquaintances sub- scribing to the Service I to the total number of acquaintances, given that the number of Service I users is n. That is ci.n/ D 2 .total number of links between Service I users/ total number of Service I users’ degrees w.r.t. G.V; E/ : The function ci.n/ is a monotonically increasing function with ci.1/ D 0 and ci.N / D 1. Figure 2.4 shows an example of ci.n/. In this case, N D 15, n D 9, and n X `D1 Di.`/ D 22; n X `D1 di.n; `/ D 12; ci.n/ D 6 11 : We assume the following power function as a property of c.n/: ci.n/ / n1ı ; (2.5) where ı is a constant. The validity of the assumption (2.5) is discussed below. Since ci.n/ will increase as the penetration of the Service I increases, ı sould satisfy ı 1. Here it is worth to note the relationship between the value of ı and topology of the social networks. If ı 0, since ci.n/ is convex, this inequality indicates that ci.n/ grows rapidly in the early stage of the Service I. In other words, there is something about clus- ter structures in that earlier subscribers to the Service I are more likely to be acquaintances of each other. If ı D 0, this means that there is no evidence of the above cluster structures. Otherwise, ı 0 is not realistic because this would mean that later subscribers of the Service I were more likely to be acquaintances of each other.
- 51. 30 M. Aida and H. Koto From (2.3) and (2.4), we can derive n X `D1 Di.`/ / n˛Cı ; .n N /: (2.6) If this holds for any n of n N , then Di.`/ / `˛Cı1 ; .` N /: (2.7) Here, let us consider three cases identified by the value of ˛ C ı 1. First, in the case of ˛ C ı 1 0, Di.`/ decreases with respect to `. Therefore, Di.`/ is the node degree of the `th earliest subscribed node in G.V; E/, and it is simultaneously the node degree of the `th largest magnitude of node degree. This correspondence is not so strict but is valid for accuracy in terms of observations in logarithmic charts. Consequently, if ˛ C ı 1 0, we have Di.`/ ' D.`/ (in terms of order); (2.8) for ` N . This relation leads to the following results. The node degree of social networks G.V; E/ obeys Zipf’s law where the expo- nent is .1 ˛ ı/, D.`/ / `.1˛ı/ ; .` N /: (2.9) People tend to subscribe to the Service I in the order of decreasing degree in G.V; E/. In other words, people with more acquaintances tend to subscribe to the service earlier. This finding about the who subscribed to the Service I service first can be consid- ered to mirror the tendency generally cited in the marketing area where people with higher sensitivity to information (more acquaintances) are more likely to try some- thing before it becomes known or popular. Next, in the case of ˛ C ı 1 D 0, Di.`/ is independent of `. It is known that if we construct an induced subgraph by selecting nodes in G.V; E/ at random, the number of links in the induced subgraph is proportional to n2 where the number of selected nodes is n [1]. This is independent of the structure of G.V; E/, and means ˛ D 1. From (2.2), the number of links should be proportional to n1C˛ (˛ ' 2=3). Therefore, the assumption of ˛ C ı 1 D 0 contradicts the observed data of the actual service. Finally, in the case of ˛ C ı 1 0, people tend to subscribe to the Service I in the order of increasing degree in G.V; E/. In other words, people with fewer acquaintances tend to subscribe to the service earlier. This result contradicts our personal experience. From the above considerations, we regard the assumption ˛ C ı 1 0 as being valid.
- 52. 2 Structure and Dynamics of Social Networks Revealed 31 log(rank order of degree) e e r g e d ( g o l o ) s t n e m e l e f gradient: log(degree of elements) m e l e f o r e b m u n ( g o l ents) gradient: Fig. 2.5 Two points are extracted from data that satisfies Zipf’s law (left), and they are plotted to give the distribution of degree (right) If the distribution of the degree of nodes in the graph representing social networks follows Zipf’s law, social networks can be taken as being scale-free. A scale-free network is a graph in which the distribution of the degree of the nodes follows a power law [6,7], p.k/ / k ; (2.10) where k is the degree of a node, p.k/ is the number of nodes with degree k, and 0 is a constant. Assume that D.`/ follows a Zipf distribution with a gradient of ˇ (where ˇ D 1 ˛ ı 0) as D.`/ D C `ˇ ; (2.11) where C is a constant. Consider ` and j for which D.`/ D k and D.j/ D k 1, then ` D C1=ˇ k1=ˇ ; j D C1=ˇ .k 1/1=ˇ : (2.12) Since p.k/ is j ` when D.`/ D k, p.k/ D C1=ˇ n .k 1/1=ˇ k1=ˇ o ' C1=ˇ k1=ˇ 1 ˇ k D O.k.1=ˇC1/ /: (2.13) Hence, the graph representing social networks is a scale-free graph whose exponent, , is D 1 ˇ C 1 D 1 1 ˛ ı C 1: (2.14)
- 53. 32 M. Aida and H. Koto Assumptions From Fig. 2.12 in Appendix A, the volume of email traffic is proportional to jEi.n/j. From Fig. 2.2, jEi.n/j D O.n1C˛ /, .˛ ' 2=3/. ci.n/ / n1ı , .ı 1 ˛/. Results The sequence of subscription to the Service I is the sequence of the magnitude of the degree in G.V; E/, Di.`/ ' D.`/ (in terms order) for ` N . The degree of nodes obeys Zipf’s law: D.`/ / `.1˛ı/ ; .` N /: The distribution of the degree of nodes in G.V; E/: p.k/ D O.k /; D 1 1 ˛ ı C 1 Fig. 2.6 The assumptions made in the analysis of service I data and the results The assumptions made in the above discussion and its results are summarized in Fig. 2.6. Although the above discussion does not lead to a specific value for ı, ı should satisfy ˛ C ı 1 0. The fact that ˛ C ı 1 indeed holds will be supported along with the assumption of ci.n/ in the next section through an analysis of the Service III. 2.4 Analysis of Social Networks Based on the Number of SNS Users In this section, we investigate the structure of social networks G.V; E/ from a differ- ent viewpoint, i.e., data generated by the Service III. In addition, by combining these results with the results of our analysis of Service I data, we clarify the details of the social network model including the verification of our assumption of the power law of ci.n/ and the determination of the value of . 2.4.1 Analyzed Data Service III is Japan’s largest social networking service provided by mixi, Inc. [9]. For a person to become a member of Service III, he or she needs to be invited to join by an existing member. Although this is a system where only those invited by
- 54. 2 Structure and Dynamics of Social Networks Revealed 33 0 500000 1000000 1500000 2000000 0 100 200 300 400 500 600 700 Number of mixi users Days from the start of service 1000 10000 100000 1000000 10000000 10 100 1000 Number of mixi users Days from the start of service Fig. 2.7 Growth in the number of service III users existing members may join, the number of users is growing rapidly due to the fact that the mechanism of existing members inviting new people to join is functioning well. The Service III started in February 2004. The number of users reached one million on August 1, 2005, and two million on December 6, 2005. While it took 17.5 months for the number of users to reach one million, it took only 4 months for the number to grow by another million. Because of the following characteristics of the growth in the number of users, Service III data is useful for understanding social networks. Since the number of Service III users grew explosively over a short period of time, it can be assumed that the process behind its growth was little affected by external factors such as changes in peoples’ lifestyles. Since a person needs to be invited to join by an existing member, the process of the growth process of its popularity, i.e., number of users, is closely related to links in social networks. The left chart in Figure 2.7 shows the growth in the number of Service III users in the early days of the service after launch with 600 users. The horizontal axis is the number of days elapsed since the start of the service. The vertical axis is the number of Service III users. The right chart is a double logarithmic chart. The lines with the gradient of 3 are shown for reference. It was reported that the number of Service III users grew exponentially [10]. Excluding the very early days, when the growth depended on the initial conditions, it can be seen that the growth in the number of users was time to the power of three. 2.4.2 Growth in the Number of SNS Users and Social Networks Let m.t/ be the number of Service III users at time t, and assume that the following holds: m.t/ / t3 : (2.15)
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- 60. This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title: El Tesoro de Gastón: Novela Author: condesa de Emilia Pardo Bazán Illustrator: José Passos Release date: May 26, 2017 [eBook #54791] Most recently updated: October 23, 2024 Language: Spanish Credits: Produced by Carlos Colón, Nahum Maso i Carcases, Josep Cols Canals, University of Toronto and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive) *** START OF THE PROJECT GUTENBERG EBOOK EL TESORO DE GASTÓN: NOVELA ***
- 61. Notas del Transcriptor Se ha respetado la ortografía y la acentuación del original. Los errores obvios de puntuación y de imprenta han sido corregidos. Las páginas en blanco presentes en el original han sido eliminadas en la versión electrónica. El índice se encuentra al final del libro. Ir al Índice
- 62. COLECCIÓN ELZEVIR ILUSTRADA VOLUMEN SEXTO El Tesoro de Gastón
- 63. Colección Elzevir Ilustrada VOLÚMENES PUBLICADOS I.—M. Hernández Villaescusa.—Oro oculto, novela. II.—Vital Aza.—Bagatelas, poesías. III.—Alfonso Pérez Nieva.—Ágata, novela. IV.—Nilo María Fabra.—Presente y futuro. Nuevos cuentos. V.—Federico Urrecha.—Agua pasada. (Cuentos, bocetos y semblanzas). VI.—Emilia Pardo Bazán.—El Tesoro de Gastón, novela. EN PRENSA M. Morera y Galicia.—Poesías, con un prólogo de Antonio de Valbuena. Enrique R. de Saavedra, duque de Rivas.—Cuadros de la fantasía y de la vida real. EN PREPARACIÓN Juan Gualberto López Valdemoro, conde de las Navas.—El Procurador Yerbabuena, novela. Antonio de Valbuena.—Santificar las fiestas, cuentos. Carlos Frontaura.—El cura, el maestro y el alcalde. Miguel Ramos Carrión.—Zarzamora, novela.
- 64. Y OTROS DE Altamira (Rafael). Aza (Vital). Becerro de Bengoa (Ricardo). Liniers (Santiago). Marina (Juan). Oller (Narciso). Pérez Zúñiga (Juan). Thebussem (Dr.) Valera (Juan), etc., etc.
- 65. Emilia Pardo Bazán El Tesoro de Gastón Novela Ilustraciones de JOSE PASSOS Con licencia del Ordinario
- 66. BARCELONA JUAN GILI, LIBRERO 223, CORTES, 223 MDCCCXCVII
- 67. ES PROPIEDAD
- 69. I La llegada Cuando se bajó en la estación del Norte, harto molido, á pesar de haber pasado la noche en wagon-lit, Gastón de Landrey llamó á un mozo, como pudiera hacer el más burgués de los viajeros, y le confió su maleta de mano, su estuche, sus mantas y el talón de su equipaje. ¡Qué remedio, si de esta vez no traía ayuda de cámara! Otra mortificación no pequeña fué el tener que subirse á un coche de punto, dándole las señas: Ferraz, 20... Siempre, al volver de París, le había esperado, reluciente de limpieza, la fina berlinilla propia, en la cual se recostaba sin hablar palabra, porque ya sabía el cochero que á tal hora el señorito sólo á casa podía ir, para lavarse, desayunarse y acostarse hasta las seis de la tarde lo menos... En fin, ¡qué remedio! Hay que tomar el tiempo como viene, y el tiempo venía para Gastón muy calamitoso. Mientras el simón, con desapacible retemblido de vidrios, daba la breve carrera, Gastón pensaba en mil cosas nada gratas ni alegres. El cansancio físico luchaba con la zozobra y la preocupación, mitigándolas. Sólo después de refugiado en su linda garçonnière; sólo después de hacer chorrear sobre las espaldas la enorme esponja siria, de mudarse la ropa interior y de sorber el par de huevos pasados y la taza de té ruso que le presentó Telma, su única sirviente actual, excelente mujer que le había conocido tamaño; sólo en el momento, generalmente tan sabroso, de estirarse entre blancas sábanas después de un largo viaje, decidióse Gastón á mirar cara á cara el presente y el porvenir. Agitóse en la cama y se volvió impaciente, porque divisaba un horizonte oscuro, cerrado, gris como un día de lluvia. Arruinado, lo
- 70. estaba; pero apenas podía comprender la causa del desastre. Que había gastado mucho, era cierto; que desde la muerte de su madre llevaba vida bulliciosa, descuidada y espléndida, tampoco cabía negarlo. Sin embargo, echando cuentas, (tarea á que no solía dedicarse Gastón), no se justificaba, por lo derrochado hasta entonces, tan completa ruina. El caudal de la casa de Landrey, casi doblado por la sabia economía y la firme administración de aquella madre incomparable, daba tela para mucho más. ¡Seis años! ¡Disolverse en seis años, como la sal en el agua, un caudal que rentaba de quince á diez y siete mil duros! Acudían á la memoria de Gastón, claras y terminantes, las palabras de su madre, pronunciadas en una conferencia que se verificó cosa de dos meses antes de la desgracia. —Tonín,—había dicho cariñosamente la dama,—yo estoy bastante enfermucha; no te asustes, no te aflijas, querido, que todos hemos de morir algún día, y lo que importa es que sea muy á bien con Dios; lo demás... ¡ya se irá arreglando! Siento dejarte huérfano en minoría, pero pronto llegarás á la mayor edad, y así que dispongas de lo tuyo, acuérdate de dos cosas, hijo... Que ni hay poco que no baste ni mucho que no se gaste, y... que no debemos ser ricos... sólo... ¡para hacer nuestro capricho, olvidándonos de los pobres y del alma! Quedan aumentadas las rentas... gracias á que no he fiado á nadie lo que pude hacer yo misma... ¡y eso que soy una mujer, una ignorantona, una infeliz! Tú, que eres hombre, y que recibes doblado el capital, puedes acrecentarlo, sin prescindir de... ¡de que hay deberes, para un caballero sobre todo!... ¡y de que la fortuna se nos da en depósito, á fin de que la administremos honradamente!... ¿Verdad, Tonín, que vas á pensar en esto que te he dicho... así... así que no estemos... juntos? Dame un beso... ¡Ay!... ¡Cuidado, que por ahí anda la pupa! Y Gastón, de pronto, sintió como los ojos se le humedecían, acordándose de que el ¡ay! de su madre había delatado, por primera vez, la horrible enfermedad cuidadosamente oculta, el zaratán en el seno.
- 71. Poco después la operaban, y no tardaba en sucumbir á una hemorragia violenta... y Gastón veía á su madre tan pálida, tendida en el abierto ataúd, y recordaba días de llanto, de no poder acostumbrarse á la orfandad, á la soledad absoluta... Después, con la movilidad de los años juveniles, venía el consuelo, y con la mayor edad, el gozo de verse dueño de sus acciones y de su hacienda, ¡libre, mozo, opulento! Dando una vuelta repentina en la cama, lo mismo que si el colchón tuviese abrojos, Gastón volvía á rumiar la sorpresa de haber despabilado tan pronto la herencia de sus mayores. —¡Si no es posible humanamente!—calculaba.—¡Si no me cabe en la cabeza! Vamos á ver; yo no soy un vicioso; no he jugado sino por entretenimiento; no he tenido de esos entusiasmos por mujeres pagadas, en que se consumen millones sin sentir. ¿Qué hice, en resumidas cuentas? Vivir con anchura; pasarme largas temporadas en el extranjero, sobre todo en el delicioso París; comer y fumar regaladamente; divertirme como joven que soy; pagar sin regatear buenos cocheros y caballos de pura raza, cuentas de sastre y de tapicero, de joyero y de camisero, de hotel, de restaurant... Todo ello, aunque se cobre por las setenas, no absorbería ni la tercera parte de mi caudal... oh, eso que no me lo nieguen. ¡Aunque me lo prediquen frailes descalzos! Me sucede lo que á la persona que ha dejado en un cajón una suma de dinero, no sabe cuánto, pero volviendo á abrir el cajón nota que hace menos bulto, y dice: «Gatuperio...» Aquí Gastón suspiró, abrazó la almohada buscando frescura para las mejillas, y pensó entrever, como filtrado por las cerradas maderas de las ventanas, un rayito de luz. —El caso es que yo fuí bien prudente. De imprevisor nadie podrá tacharme. ¿Á quién mejor había de confiar mis negocios, y la gestión y administración de mis bienes, que á don Jerónimo Uñasín? Un viejo tan experto, con tal fama de seriedad y honradez en los negocios; y además, de una condición encantadora; nunca le pedía yo con urgencia dinero, que á vuelta de correo no me lo girase sin objeción alguna... En lo que no tiene disculpa don Jerónimo, es en
- 72. no haberme avisado de que mis gastos eran excesivos; de que á ese paso me quedaba como el gallo de Morón... Al hacer reflexión tan sensata, por primera vez el incauto mozo sintió algo que podría llamarse la mordedura de la sospecha y el aguijón del reconcomio. Evocó el recuerdo de la cara de don Jerónimo y se le figuró advertir en ella rasgos del tipo hebreo, la nariz aguileña, de presa, la boca voraz, los ojos cautelosos y ávidos... Las palabras de su madre resonaron de nuevo en su corazón olvidadizo: «No he fiado á nadie lo que pude hacer yo misma...» Al cabo se durmió. Á las seis, obedeciendo órdenes, Telma vino á despertarle de un sueño agitado, lleno de pesadillas; arreglóse á escape, y á las siete menos cuarto conferenciaba con don Jerónimo. Más de una hora duró la entrevista, de la cual salió Gastón con la
- 73. sangre encendida de cólera y el espíritu impregnado de amargura. La venda se había roto súbitamente y Gastón veía,—¡á buena hora! —que aquel tunante de apoderado general era el verdadero autor de su ruina. Á preguntas, reconvenciones y quejas, sólo había respondido don Jerónimo con hipócrita y melosa sonrisilla, que provocaba á chafarle de una puñada los morros. —¿Qué quería usted que hiciese?—silbaba el culebrón.—¿Pues no estaba usted pidiendo fondos y fondos á cada instante? ¿Pues no era usted mayor de edad, dueño de sus acciones y sabedor de á cuánto ascendían sus rentas? Usted, desde París, libranza va y libranza viene, y Jerónimo Uñasín teniendo que dejarle á usted bien, y que buscar y desenterrar las cantidades aunque fuese en el profundo infierno... ¡Bien me agradece usted los apuros que he pasado, las sofoquinas, las vergüenzas, sí, señor! ¡que vergüenza y muy grande es, á mis años, andar solicitando á prestamistas y aguantando feos! Todo lo he hecho, por ser usted hijo de los señores de Landrey, que tanto me apreciaban... Ahora conozco que me pasé de tonto, que debí cerrarme á la banda y contestarle á usted cuando me pedía monises: «otro talla, señor mío...» —Pero usted bien veía que yo me quedaba pobre,—exclamaba Gastón con indignación apenas reprimida,—y debiera usted, como persona de más experiencia, aconsejarme, llamarme la atención, advertirme... Yo le dí á usted poder ilimitado... Yo tenía depositada mi confianza en usted. —¡Sí, sí, advertir! ¡Bonito recibimiento me esperaba! Ya sé yo lo que son jóvenes contrariados en sus antojos... Y además, don Gastoncito, ¿quién me decía á mí que al echar así la casa por la ventana, no preparaba usted una gran boda? Hay en París señoritas de la colonia americana, que apalean el oro... ¡Es preciso respetar muchísimo, muchísimo la libertad de cada uno! y lamentaría toda mi vida que por mí fuese usted á perder la colocación brillante que se merece...
- 74. —Téngame Dios de su mano,—pensó Gastón al escuchar esta nueva insolencia, y conociendo que se le subía á la cabeza la ira, y las manos se le crispaban ansiosas de abofetear al judío. Al fin, con violento esfuerzo sobre sí mismo, revolviendo trabajosamente la lengua en la boca seca y llena de hiel, pronunció: —Bien, cortemos discusiones, que á nada conducen; al grano... ¿Me queda algo, lo preciso para comer? Vaciló un instante don Jerónimo, y afectó un golpe de tos, ruidosa y como asmática, antes de responder, fingiendo fatiga: —Mire usted, lo que es eso... hasta que... ¡bruum! hasta que... yo... reconozca... y liquide... ¡bruum!... los créditos... y se proceda... á la venta de... de las fincas hipotecadas... es imposible decir si el... ¡bruum! pasivo... supera al activo... Acaso tengamos déficit... pero ¡bruum! ej... ej... no será muy grande... —¿Es decir,—preguntó Gastón con temblor de labios,—que aún podrá suceder que después de venderlo todo... deba dinero? —Ej, ej... calculo que una futesa... No quiso oir más Gastón. Tomando su sombrero, despidióse con una frase bronca, y abandonó el nido del ave de rapiña á quien tarde veía el pico y las garras. En el recibimiento, mientras recogía sombrero y bastón, no pudo menos de fijarse, con penosa y estéril lucidez, en detalles que le sorprendieron: un soberbio mueble de antesala tallado, un rico tapiz antiguo, una alfombra nueva y densa como vellón de cordero, un retrato, escuela de Pantoja, una lámpara de muy buen gusto. Parecía la entrada de una casa señorial, y al acordarse de que antaño don Jerónimo se honraba con alfombra de cordelillo y sillas de Vitoria, Gastón se trató á sí mismo de majadero, no sin reprimirse para no emprenderla á palos con los muebles y con el dueño en especial... Volvió á su morada á pie, devorando la pesadumbre, queriendo sobreponerse á ella, y sin conseguirlo. Telma, solícita, le había preparado una comida de sus platos predilectos; pero no estaba la Magdalena para tafetanes, ni Gastón para apreciar debidamente el
- 75. mérito del puré de alcachofas, los langostinos en pirámide y las costilletas de cordero delicadamente rebozadas en salsa bechamela. —Hija, es preciso que me vaya acostumbrando á las lentejas y al pan seco,—respondió con un humorístico alarde cuando la vieja criada, llevándose la fuente, preguntaba con inquietud, si era que ya «tenía perdida la mano.» Y la fiel servidora, antes de cruzar la puerta, clavó en su amo una mirada perruna é inteligente, una mirada que se condolía... Vestido el frac, después de comer, Gastón dedicó la noche á intentar ver á dos ó tres personas de quienes esperaba consejo y auxilio. Á ninguna encontró en casa, y sería caso raro que lo contrario acaeciese en Madrid, donde la noche se consagra á círculos, teatros y sociedades. Rendido, harto de dar tumbos en el alquilón, se recogió á las doce y media. Una gran desolación, un pesimismo mortal le agobiaban, poniéndole á dos dedos de la desesperación furiosa. Sin duda que al siguiente día le sería fácil encontrar en casa, amables y sonrientes, á sus noctámbulos amigos; pero ¿qué sacaría de ellos? Á lo sumo... buenas palabras... ¡Ni Daroca, el bolsista; ni el flamante marqués de Casa-Planell, el riquísimo banquero; ni Díaz Carpio, el actual subsecretario de Hacienda; ni mucho menos el gomoso Carlitos Lanzafuerte, iban á abrir la bolsa y ponerla á disposición del tronado!... (Tan feo nombre se daba á sí propio Gastón).
- 76. Al dejar Telma sobre la mesa de noche la bebida usual, la copa de agua azucarada con gotas de cognac y limón, mientras Gastón, inerte, yacía en la meridiana, esperando á que se retirase la criada para empezar á desnudarse, ésta dijo no sin cierta timidez, el recelo de los criados que ven á sus amos muy tristes: —Señorito... anteayer mandó á preguntar por usted la señora Comendadora. ¿No sabe? Su tía, la del convento... Que si había vuelto ya de Francia... y que deseaba verle... Que cuando viniese, por Dios no dejase de ir, sin tardanza ninguna... —¡Bien, bien!—contestó él impaciente. Así que apagó la bujía y se tendió en la cama, la arcaica figura de la Comendadora se alzó en la oscuridad. Abandonado de todos Gastón, un instinto le impulsaba á buscar arrimo y consuelo, á desear comunicarse con alguien que le compadeciese y le amase de veras. Y su tía abuela, la Comendadora, era la única parienta cercana que tenía en el mundo.
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