Mining and analyzing social media part 2 - hicss47 tutorial - dave king

Mining and Analyzing
Social Media: Part 2
Dave King
HICSS 47 - January 2014

Agenda: Part 2

• Introduction to Social Network
Analysis Metrics
– Degrees of Separation
– Hooray for Bollywood

• Standard Measures
– Centrality
– Cohesion

• Levels of Social Network Analysis
– Facebook & Egocentric Analysis
– Searching for Cohesive Subgroups

2

Social Network Analysis
Analyzing Social Networks – The World of Metrics
Social scientists, physicists, computer
scientists, and mathematicians have
collaborated to create theories and

algorithms for calculating
novel measurements of social
networks and the people and
things that populate them.
These quantitative network metrics allow
analysts to systematically dissect the
social world, creating a basis on

which to compare networks,
track changes in a network
over time, and determine the
relative position of individuals
and clusters within a network.

3

Wide Variety of Metrics Available

4

Best Known Social Metric

5

6 Degrees of Separation
A fascinating game grew out of this discussion. One of us
suggested performing the following experiment to prove that the
population of the Earth is closer together now than they have ever
been before. We should select any person from the 1.5 billion
inhabitants of the Earth—anyone, anywhere at all. He bet us that,
using no more than five individuals, one of whom is a personal
acquaintance, he could contact the selected individual using
nothing except the network of personal acquaintances.
Frigyes Karinthy , Chains, 1929

P1

I1

I2

I3

I4

I5

P2

Degrees of separation ~ Average Path Length ~ Distance
6

Why the notoriety?
Frigyes Karinthy
1929

John Guare
1990

Stanley Milgram
1967

Duncan Watts
1998

Six Degrees of Kevin Bacon (1994)
7

Social Networks
The Oracle of Bacon

8

Oracle of Bacon gone mainstream

9

How the Oracle of Bacon Works

10

Center of the Hollywood Universe

11

of Bachchan

Aishwarya Rai
Bachchan

Amitabh Bachchan

Abhishek Bachchan

There’s a new game in town

13

The Center of Bollywood

Wikipedia Web Page

Relational DB – 627 Movies – 1061 Actors
(2010-2013)

HTML- Page Source

Pajek .NET File
14

Bipartite Network – Movies and Actors

Pajek .NET File
15

Analyzing Bollywood

16

Social Networks
Rules of Networks

• RULE 1: WE SHAPE OUR NETWORK
• RULE 2: OUR NETWORK SHAPES
US
• RULE 3: OUR FRIENDS AFFECT US
• RULE 4: OUR FRIENDS‟ FRIENDS‟
FRIENDS AFFECT US
• RULE 5: THE NETWORK HAS A LIFE
OF ITS OWN

17

Bifurcated Methodology

Local
Measures

Global
Measures

18

Walks and Paths
• Two points may be directly
connected or indirectly
connected thru a sequence of
lines called a walk.

• If points and lines are distinct it‟s
a path.
• The length of a path is the
number of edges (or lines) that
make it up.

• The shortest length is called the
distance or geodesic.

Undirected

Sample Walks
((C,A),(A,D))
((C,A),(A,B),(B,D))
((C,A),(A,D),(D,A),(A,D))

A
B

Sample Paths
((C,A),(A,D))
((C,A),(A,B),(B,D))

C
D
Directed

Sample Walks
((C,A),(A,D))
((C,A),(A,B),(B,D))

A

B

Sample Paths
((C,A),(A,D))
((C,A),(A,B),(B,D))

C

D
19

Centrality – Who is most influential?
Measure
Degree

Definition
Number of edges or links. In
degree- links in, Out-degree - links
out

Interpretation
How connected is a node? How
many people can this person reach
directly?

Reasoning
Higher probability of receiving and transmitting
information flows in the network. Nodes considered
to have influence over larger number of nodes and or
are capable of communicating quickly with the nodes
in their neighborhood.

Betweenness

Number of times node or vertex
lies on shortest path between 2
nodes divided by number of all
the shortest paths

Degree to which node controls flow of information in
the network. Those with high betweenness function
as brokers. Useful where a network is vulnerable.

Closeness

1 over the average distance
between a node and every other
node in the network

How important is a node in terms
of connecting other nodes? How
likely is this person to be the most
direct route between two people
in the network?
How easily can a node reach other
nodes? How fast can this person
reach everyone in the network?

Eigenvector

Proporational to the sum of the
eigenvector centralities of all the
nodes directly connected to it.

Measure of reach. Importance based on how close a
node is located with respect to every other node in the
network. Nodes able to reach most or be reached by
most all other nodes in the network through geodesic
paths.
How important, central, or
Evaluates a player's popularity. Identifies centers of
influential are a node’s neighbors? large cliques. Node with more connections to higher
How well is this person connected scoring nodes is more important.
to other well-connected people?

20

Cohesion – How well connected?
Cohesion

Definition

Interpretation

Reasoning

Density

Ratio of the number of edges in the
network over the total number of
possible edges between all pairs of
nodes

How well connected is the overall
network?

Perfectly connected network is called a "clique" and has a
density of 1.

Clustering

A node's clustering coefficient is the
density of it's 1.5 degree egocentric
network (ratio of connecting among
ego's alters). For entire network it is
the average of all the coefficients for
the individual nodes.

What proportion of ego's alters are
connected? More technically, how
many nodes form triangular
subgraphs with their adjacent
nodes?

Measures certain aspects of "cliquishness." Proportion of
you friends that are also friends with each other.
Another way to measure is to determine (in a undirected)
graph the ratio of the number of times that two links
eminating from the same node are also linked.

Average Path Length Average number of edges or links
(Distance)
between any two nodes (along the
shortest path)

On average, how far apart are any
two nodes?

This is synonymous with the "degrees of separation" in a
network.

Diameter

Longest (shortest path) between
any two nodes

At most, how long will it take to
reach any node in the network?
Sparse networks usually have
greater diameters.

Measure of the reach of the network

Centralization

Normalize ratio of the sum of the
Indicates how unequal the
variances of the centrality of each
distribution of centrality is in a
node from the most central node to network.
the maximum sum possible

Measures how much variance there is in the distribution
of centrality in a network. The measure applies to all
forms of centrality.

21

Generic Example for
E

B

D

A

• For each of the nodes what
is it‟s

G

–
–
–
–

F

C

H
R
I

N

P
J
O
K
L

M

Q

S

Degree Centrality
Betweenness Centrality
Closeness Centrality
Eigenvector Centrality

• For the entire network what
is it‟s
–
–
–
–

Degree Centralization
Betweenness Centralization
Closeness Centralization
Eigenvector Centralization
22

Visualizing and Analyzing with ORA

23

Centrality – Who is most important?
E

B

D

A

Eigenvector
G

F

C

Betweenness
H

Closeness

R
I

N

Degree

P
J
O
K
L

M

Q

S
24

Cohesion – How well connected?
E

B

D

A

G

F

C

H
R
I

N

P
J

O
K
L

M

Q

Measure
Value
Network Size
19
Average Degree
3.37
Degree Centralization
0.22
Betweenness Centralization
0.48
Closeness Centralization
0.27
Eigenvector Centralization
0.56
Clustering Coefficient
0.43
Density
0.19
Average Distance
3.06
Diameter
8
Number of Unreachable Nodes
0

Node
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S

Clustering
0.67
0.67
0.00
0.40
1.00
0.50
0.50
0.10
0.33
0.29
0.67
0.67
0.33
0.67
1.00
0.67
0.00
NA
NA

S
25

The World of Facebook
Active Users
1.2B

18%

Likes Daily

4.5B

67%

Photo Uploads

Mobile Users
.9B

45%

Pieces of Content
Shared Daily

4.8B

94%

Of Total Web
Page Views

Logon Daily
.7B

25%

New Profiles
5/second

1/5 on FB

Avg Time
Per Visit
20 minutes

Sex Ratio

Europe

Age 24-34

53%F/47%M

.2B Users

30% of users

300M/day

26

Facebook in the World

facebookstories.com/stories/1574/
#color=language-official&story=1&country=SA
27

Your World of Facebook

app.thefacesoffacebook.com

apps.facebook.com/challenger_meurs/
?fb_source=appcenter&fb_appcenter=1

Geographical.cz/socialMap/

apps.facebook.com/touchgraph/
28

Egocentric Network – Facebook Example

29


30

Netvizz v0.93

.gdf (GUESS) file format

One simple way to generate SNA data from Facebook
31

Social Network
Cleansed-Augmented Guess .GDF File used for analysis

guess.wikispot.org/The_GUESS_.gdf_format
32

Egocentric Networks – by Degree

1.5

1.0

2.0
Ego
(Ego‟s) Alter
Alter‟s Alter

33


34


Getting Started With The Gephi
Network Visualisation App
– My Facebook Network, Part I
blog.ouseful.info/2010/04/16
/getting-started-with-gephi-networkvisualisation-app-myfacebook-network-part-i/

35

Matrix Representation

Graph Representation

PL = N(N-1)/2 = 3081 Ego Density = L/PL = 312/3081 =.10

36

(Avg 7.9)

(Avg 32.0)

(Avg .26)

(Avg 2.7)

(Avg 7.9)

(Avg .66)

37

Another Analytical Alternative - NodeXL

38

Facebook Analysis
The emergence of online social networking services over
the past decade has revolutionized how social scientists
study the structure of human … previously invisible social
structures are being captured at tremendous scale and with
unprecedented detail.

Accessed within 28 days of May ‟11
At least one friend
Over 13 years of age

39

•

Nearly fully connected, with 99.91% of
individuals belonging to a single large
connected component

•

Confirm „six degrees of separation‟
phenomenon on a global scale. Second, by
studying

•

While the Facebook graph as a whole is
clearly sparse, the graph neighborhoods of
users contain surprisingly dense

•

Clear degree assortativity.

•

Strong impact of age on friendship
preferences as well as a globally modular
community structure driven by nationality, but
no gender homophily.

40

Facebook Analysis

14% for 100

Assortativity

P(F|F) = .52
P(F|M) = .51

41

Facebook Analysis
Average
4.7

Average
4.3

World 92% 99.6%
US
96% 99.7%

42

Looking for Cohesive Subgroups

43

Sociology
Cohesive Subgroups

Many individuals have large clusters of friends corresponding to well-defined
foci of interaction in their lives, such as their cluster of co-workers or the cluster
of people with whom they attended college. Since many people within these
clusters know each other, the clusters contain links of very high
embeddedness, even though they do not necessarily correspond to particularly
strong ties.
44

Cohesive Subgroups
E

B

D

A

•
•

G

In a complete graph all the nodes are adjacent to
one another
A network is connected if every two nodes in the
network are connected by some path in the network

F

C

–
H

R
I

N

•

A graph G has components G1 and G2 if no
(undirected) path exists between any node in G1 to
any node of G2 (component is an isolated
subgraph)

•

P

A link is a bridge in a network if it‟s removal
increases the number of components in the network

J

O
K
L

A directed graph is strongly connected if and only if for
every pair of vertices x , y, there is a directed path from x to y
and a directed path from y to x between them. It is weakly
connected if there is at least an undirected path for every
pair of vertices.

M

Q

S
45

Cohesive Subgroups
E

B

D

A

• A clique is a maximal complete subnetwork
containing three vertices or more.
G

• n-clique is a maximal subnetwork in which
the maximum path length for connection is
“n” (e.g. 2-clique has nodes connected by
paths of 1 or 2 lengths).

F

C

H
R
I

N

P
J

O
K
L

M

Q

• A k-core is a maximal subnetwork in which
each vertex has at least degree k within the
subnetwork (e.g. 3-core)

• Girvan-Newman Algorithm breaks
complex networks into “communities” by
removing edges (betweenness) resulting in
fragmentation

S
46

It’s a Small World after all, or is it?

6.0 vs. 4.7
48

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