An improvised model for identifying influential nodes in multi parameter social networks

Dhinaharan Nagamalai et al. (Eds) : ACITY, WiMoN, CSIA, AIAA, DPPR, NECO, InWeS - 2014
pp. 25–30, 2014. © CS & IT-CSCP 2014 DOI : 10.5121/csit.2014.4503
AN IMPROVISED MODEL FOR
IDENTIFYING INFLUENTIAL NODES IN
MULTI-PARAMETER SOCIAL NETWORKS
Abhishek Singh1
and A. K. Agrawal2
1,2
Department of Computer Engineering, IIT(BHU) Varansi
abhishek.singh.cse09@iitbhu.ac.in
akagrawal.cse@iitbhu.ac.in
ABSTRACT
Influence Maximization is one of the major tasks in the field of viral marketing and community
detection. Based on the observation that social networks in general are multi-parameter graphs
and viral marketing or Influence Maximization is based on few parameters, we propose to
convert the general social networks into “interest graphs”. We have proposed an improvised
model for identifying influential nodes in multi-parameter social networks using these “interest
graphs”. The experiments conducted on these interest graphs have shown better results than the
method proposed in [8].
KEYWORDS
Viral Marketing, Community Detection, Influence Maximization
1. INTRODUCTION
In today’s era of the internet, the enormous growth and penetration of social networks into
people’s daily lives has brought a number of opportunities and challenges. It is not only a way to
connect to the rest of the world but has also become an integral part of business, economy,
politics and almost all such fields.
Identifying community structure [10] has been a central area of research in identifying groups in
the network based on multiple factors such as common interests, friendship, organizations etc
among the ‘actors’. These communities are important as they can be viewed as a platform for
sharing knowledge, data, emotions, sentiments etc. Another application of social network
analysis has been viral marketing [] which is a very crucial area of research in business analytics.
Viral marketing is an advertisement technique where one identifies a subset of ‘actors’ of the
social network so as to obtain a “word of mouth” effect in promoting the product.
A major task in tackling both these problems is identifying influencers in the network, as whether
it is the survival of a community or spreading of an innovation/idea/product in a network, there’s
always a need for certain ‘actors’ who have influence over the rest of the community. This can be
seen in viral marketing as companies trying to identify a seed set of individuals to introduce their
product so as to have as much spread of word as possible. In terms of community detection, a

26 Computer Science & Information Technology (CS & IT)
certain set of individuals that share interests can be seen influencing each other. For example, an
individual who shares interests in terms of his movie preferences with another individual would
be compelled to watch a new movie if he/she sees positive feedback from the other. When this
happens, the community detection algorithms increases the parameter used to represent the
common interests among a certain set of individuals which results in detecting the community.
So, although both community detection and viral marketing are different areas, the underlying
problem in both the cases is the same. This is the problem of maximizing the spread of influence
in a network.
Formally, the problem of Influence maximization involves finding few initial users in an online
social network to adopt an innovation and spread the information, so that the influence of
innovation or product in the network is maximized. Influence maximization is a problem applied
not only to tasks related to social networks but can be used for different other applications.’
Finding these 'few initial users' in these large networks is the major challenge of the problem and
for which, huge amount of data is needed to be processed. Not only the processing of huge
amount of data is required, timeliness of the processes are also important. For this, the time
complexity of the process should be small. The most popular approaches in this area are greedy
algorithm and/or optimizations to the greedy algorithms.
It was observed that the individuals are connected to many others based on different interests. So
a product/idea/event, which is to be 'spread' in the network, belong to a particular community of
the individual only. So, instead of targeting the entire network to find 'influential seeds', one can
find the community first, where the probability of spreading is high and subsequently finding the
'seed'/'seeds'. In this paper, we propose an improvement of the three methods for choosing the
seeds by using community detection methods. The approaches are discussed in the next sections.
In our approach, we emulate relationship between community detection and viral marketing.
The rest of the paper is organized as follows: section 2 discusses about the related works, section
3 describes our method, section 4 provides experimental results and section 5 concludes and
discusses the future aspect of the work.
2. RELATED WORK
The concept of spreading of an idea, or an innovation or influence for that matter was first studied
in the field of economy, giving birth to viral marketing. Several models were proposed to
simulate this process. There are two models in particular have gained widespread acceptance.
These are the Linear Threshold Model and the Independent Cascade Model. The Linear
Threshold model states that every node in a network has some threshold which is needed to be
achieved after which it can become active. The Independent Cascade model on the other hand
gives a probabilistic methodology to this. It proposes that any active node in a network would get
a dingle chance to activate an inactive node, which it can do with certain probability. The
problem of Influence Maximization was first studied by Domingos and Richardson [1][2].
Although there attempts at solving this problem were probabilistic. Since Domingos and
Richardson studied the problem of Influence Maximization, the other researchers [5][6][7] have
proposed greedy approaches rather than the probabilistic approach suggested by the formers. In
[3], Kempe et.al, proposed a greedy approach to solve what they viewed as a discrete

Computer Science & Information Technology (CS & IT) 27
optimization problem. After this several modifications and improvements have been proposed
over this original approach.
In 2010 Tieyun Qian et.al [8] proposed a different approach towards studying the same problem
by identifying seed nodes in implicit social networks. The suggested approach uses the Reverse
Nearest Neighbours logic presented by [4], and build on that by defining Social Network
Potential of an individual in a network. Inspired by this idea, we propose a new model to identify
influential nodes and understand the spread of influence in a network where the connections
between actors incorporate various factors such as the reasons for these connections and how
strong these connections are.
3. PROPOSED METHOD
In this work we propose a model based on the method of [8]. As discussed in section 1 it was
observed that the actors in the social networks are connected to each other for various
interest/reasons. So a product/idea/event, which is to be 'spread' in the network, may be of interest
to a particular set of individuals only. Here we propose a model for the Influence Maximization
problem taking into account the specific area which may be of interest to one who wants to
influence the network, out of the available areas.
Generally, the social networks are represented as graphs where the nodes are actors and the edges
represent the connections between these actors. This representation of the edge is a accumulation
of multiple parameters on which the social network is based. These parameters are of diverse
nature like location, interests, likes etc. The application of any method traditionally involves
considering all the above mentioned parameters instead of focusing on a particular interest. So in
our model we converted the traditional social graph into “interest graph”, which represents a
particular interest(s) of the network. By this the volume of the network and the parameters of the
network are reduced subsequently bringing down the time complexity and the computational
overhead of applying the method on the original graph. An overview of the proposed model is
shown in Figure 1.
Figure 1. Pictorial description of the proposed model
The model shows a social network, for example a blogger network. Now actors in a blogger
network may be connected to each other through links that represent multiple shared interests.

The graph extracted from such network has edges that account for a number of parameters which
may or may not be of interest. Hence it is required that the graph be filtered to form an interest
graph containing edges with weights specific to the interest. Once we have this graph we can
move forward with the basic algorithm as proposed by [8]
4. EXPERIMENT
The data used in [11], forms the basis of our experiments. The data contains information about
blogs and bloggers from a particular organization. The author of the blog use different tags for
each blog entry they make. These blogs are represented as a graph where the blogs are the nodes
and the edges are defined as the relationship between the blogs. This relationship is defined by
the common tags giving weightage to particular tag which in this case represents the interests of
the authors.
Figure 2. An example edge in the multi-parameter network
Any graph which represents this blog network can be defined by representing the blogs as nodes
and the tags can be used to represent the weightage between the nodes. For converting this graph
into “interest graph” we have given weightage to a particular tag in which one is interested. For
example, let there be two blogs b1 and b2 having the tags{t1,t2,t3} and {t1, t4} respectively as
shown in fig 2, then the nodes represent b1 and b2, and the weightage of the edge between b1 and
b2, will be calculated as:
The graph so prepared is of 500 nodes and 87436 edges, by taking the first 500 nodes and their
connections from the original dataset. The weights of this newly formed graph are then used as
similarity measure for the nearest neighbourhood algorithm [4]. Then we use the methods
explained in[8], to calculate the SNP values for the actors and find the desired set of seed nodes.
5. RESULTS
Table 1. Top 5 users for k=1
User-Id R1NN SNP
#211
8 22 41 45 61 100 107 137 157 169 171 175 186 209 227
247 249 280 295 296 297 298 312 316 337 359 380 391
429 435 437 455 461 481
34
#12 5 8 9 23 34 40 41 108 114 129 162 169 171 209 216 217
229 232 243 245 297 311 337 345 385 391 408 428 455
481
32

Computer Science & Information Technology (CS & IT) 29
#119
2 29 41 142 169 171 209 217 239 243 245 247 263 271 297
300 337 355 368 370 383 391 401 409 417 421 425 454
455 481 485
31
#65 2 26 33 39 43 79 82 115 122 136 203 205 240 243 250 264
271 295 311 333 336 347 377 398 399 472 475 485
28
#327 4 16 23 27 32 47 56 92 94 103 129 130 154 163 181 182
186 197 217 228 283 339 375 385 418 427 457
27
6. CONCLUSION
In this work, we have proposed an improvised model for Influence Maximization in a general
social network with edges having weights that are combination of multiple parameters. In such
networks, connection between any two actors may be seen due to multiple shared interests. Thus,
application of any algorithm on such a graph directly would not be completely realistic. Our work
has addressed this problem by isolating these parameters by creating “interest graphs”.
The results so obtained are not very different from those obtained on the original graph, but the
isolation of parameters has shown improvements in terms of the computational and time
complexity requirements of the algorithm. Although the original algorithm would work perfectly
in case of single parameter connections, we have proved that using “interest graphs” improves the
accuracy and efficiency of the algorithm in multi parameter connection graphs.
As mentioned in the introduction, the fields of viral marketing and community detection are
connected. Hence, as part of our future work we plan to use this hypothesis and work towards
improving our model by incorporating community detection in this work.
REFERENCES
[1] P. Domingos & M. Richardson. “Mining the network value of customers”, 2001
[2] M. Richardson & P. Domingos. “Mining Knowledge-Sharing Sites for Viral Marketing”, 2002.
[3] D. Kempe, J. Kleinberg, & E. Tardos. “Maximizing the spread of influence through a social
network”, 2003
[4] S. M. Flip Korn & S. Muthukrishnan. “Influence sets based on reverse nearest neighbour queries”,
2000
[5] W. Chen, Y. Wang, & S. Yang. “Efficient influence maximization in social networks”, 2009.
[6] J. Leskovec, A. Krause, C. Guestrin, C. Faloutsos,J. VanBriesen, & N. Glance. “Cost-effective
outbreak detection in networks”.
[7] W. Chen, Y. Wang, & C. Wang. “Scalable Influence Maximization for Prevalent Viral Marketing in
Large-Scale Social Networks”, 2010.
[8] Tieyun Qian & Jiangbo Liu“Influence Maximization through Identifying Seed Nodes from Implicit
Social Networks”, ICUIMC’10 proceedings
[9] en.wikipedia.org/wiki/Viral_marketing
[10] http://en.wikipedia.org/wiki/Community_structure

[11] Nitin Agarwal, Huan Liu, Lei Tang & Philip S. Yu “Identifying influential blogger in a community”,
in proceedings of the 1st International Conference on web search and data mining(WSDM ‘08), PP
207-218,Feb 11-12 2008, Stanford, California
AUTHORS
Abhishek Singh is a post graduate student at the department of computer engineering, IIT-
BHU. His area of interests are social networks, data mining, graph theory.
Prof. A. K. Agrawal is the head of department of Department of Computer Engineering at
IIT-BHU. His areas of interest include database systems, theory of computation, compiler
design and graph theory.

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