Volumn 5


Rajeshri Puranik
Assistant Professor
Department of Mathematics
P.I.E.T Nagpur

Dr. Sharad Pokley
Associate Professor
Department of Mathematics
K.I.T.S Ramtek


The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics. The network by mean social graph has been referred to as “the global mapping of everybody and how they’re related”. on the other hand the term text analytics describes a set of linguistic, statistical, and machine learning techniques that model and structure the information content of textual sources for business intelligence, exploratory data analysis, research, or investigation. The focus of this research work is to optimize a social networking model derived from set of influencing entities for the two dimensionalities graph and text based on the working of two giant competitors Twitter and Facebook.

1. Introduction:

The advent of online social networks is changing behavior in many contexts allowing decentralized interaction among larger groups and fewer geographic constraints. The structure and complexity of these networks have grown rapidly in recent years. At the same time, online networks are collecting social data at unprecedented scale and resolution, making social networks visible that in the past could only be visible via in-depth surveys. Today, millions of people live Digital traces on their personal social networks in the form of text messages on mobile phones, updates on Facebook or Twitter and so on. The Mathematical analysis of networks is one of the great success stories of applying the Mathematical sciences to an engineered system, going back to the days when AT&T Networks were designed and operated based on Graph Theory, Probability, Statistics, Discrete Mathematics and optimization. However, since the rise of the internet and Social Networks, the underlying assumptions in the analysis of networks have changed dramatically. The abundance of such Social Network data, and theincreasing complexity of Social Networks, is changing the face of Research on social networks. This change presents both opportunities and challenges for mathematical and statistical modeling. One example of how the Mathematical sciences have contributed to the new opportunity is the significant amount of recent work focused on the development of random-graph models that capture some of the qualitative properties observed in large scale network data. The mathematical models developed, help us to understand many attributes of social network. One such attribute is the degree of connectivity of a network, which in some cases reveals the smallness of world, in which very distant parts of a population are connected via surprisingly short paths. These short paths are surprisingly easy to find which has led to the success of decentralized search algorithms.

Another important direction is the development of models of Contagion and network processes. Social Networks play a fundamental role in spreading information, ideas and influence. Such contagion of behavior can be beneficial when a positive behavior change spreads from person to person, but it can also produce negative outcomes, as in cascading failures in financial markets. Such concepts open the way to epidemiological models that are more realistic than the “Bin” models that do not take the structure of interpersonal contracts into account. The level of complexity in influencing and understanding such Contagion phenomenon rises with the size and complexity of the social network. Mathematical models have great potential to improve our understanding of this phenomenon and to inform policy discussions aimed at enhancing system performance. Now-a-days social networking sites have very much importance in our daily life. There are various entities which affects these social networking sites like Leaders and followers, Whistle blowers, and so on. In this paper we have discussed various entities affecting social networking sites like Face book & Twitter. The outline of the paper is as follows. In section II we have discussed various entities (considering as social networking variables) affecting social networking sites like Face book & Twitter. Objective of this research is discussed in section III. Section IV concludes the paper.

2. Social networking variables

i. Whistleblower:

A Whistle blower is a person who exposes any kind of information or activity that is deemed illegal, dishonest, or not correct within an organization that is either private or public. Whistle blowing is providing a solution to resolve such situations: it opens nonexistent or hidden information sources and channels. Nowadays, social networking services (SNS) have become so popular that they have been integrated
to our daily life. In this paper [1] the authors have conducted a preliminary study on a whistle blowing network, constructed from 328472 whistle blowing (complaining) reports. The findings provide a deep understanding of the whistle blowing network, and can give guidelines to improve the system fighting against malicious information.

ii. Leaders and Followers:

Leaders in social networks are users whose opinions are highly influential on those of others.
Followers in social networks are users whose opinions are highly influenced by those of leaders.
Identifying leaders and followers in online social networks is important for various applications in
many domains such as advertisement, community health campaigns, administrative science, and even politics. The authors developed a Longitudinal User Centered Influence (LUCI) model that takes as input user interactions in an online social network to group users into four categories Introvert Leaders (IL), Extrovert Leaders (EL), Followers (F), and Neutrals (N).

iii. Inverse Influence:

In online social networks, social influence of a user reflects his or her reputation or importance in the whole network or to a personalized user. Social influence analysis can be used in many real
applications, such as link prediction, friend recommendation and personalized searching. Personalized Page Rank, which ranks nodes according to the probabilities that a random walk starting from a personalized node stops at all nodes, is one of the most popular metrics for influence analysis. In this paper the authors studied the problem of inverse influence for a personalized node in a graph.

iv. Recommenders:

In online social networks (OSNs), it is an open challenge to select proper recommenders for predicting the trustworthiness of a target. In real life, people who are close and influential to us can usually make more proper and acceptable recommendations. Based on this observation, in [4] the authors presented the idea of recommendation-aware trust evaluation (RATE).

v. Influence Maximization:

VIRAL MARKETING – A marketing strategy that focuses on spreading information and opinions about a product or service from person to person, especially by using unconventional means such as the internet or email. Now-a-days, the viral marketing has been extensively increased on online social networks, thus increasing the research work on the influence maximization algorithms in social networks. Motivated
by this viral marketing strategies, many of the researches proposed few fundamental algorithms to find the subset of individuals to promote a product where the goal is to trigger maximum number of individuals in the network. The authors proposed a new diffusion model and apply it to solve the influence maximization problem.

vi. Immunization:

Along with the rapid development of social networks, social network worm has constituted one of the major internet security problems. These worm poses more and more security threats to the Internet because of the following characteristics. First, they rely on the information contained in the victim machine to locate new targets, which makes them propagate more efficiently than traditional Internet worms. Second, they rely on the trust between the users on social networks to propagate themselves, which makes them spread more widely than traditional Internet worms. The authors studied how to prevent the propagation of social network worms through the immunization of key nodes.

vii. Influence:

Quantifying the influence of one node exerts on another in a social network by using directed
information for a simple two node network that models two users in a Twitter network in which one user influences the other user through her tweets. The authors are interested in a mathematical understanding of the problem of inference of influence graphs in social networks. They focus on a simple, two-node social network that can be interpreted as a model for interactions on a Twitter network. In this paper, the influence is computed by characterizing the directed information between the input and output of buffer less single-server timing queue (SSTQ).

viii. Information dissemination:

Social networks are deeply fused into our daily lives for people to recognize and acquire information or content through social connections. Some content creators may want to control the dissemination process due to the authorization, value, cost or resources associated with the created contents. For example, a merchant may distribute a certain number of coupon brochures to potential customers; a bookseller delivers some free books to book fans; a conference organizer may send a limited number of invitations to potential interested people. We call such information dissemination process as Semi controlled Authorized Information Dissemination (SAID). The authors investigated the Semi controlled Authorized Information Dissemination (SAID) in Content-based Social Networks.

ix. Community Detection:

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relative features of graphs representing in real systems is community detection. The Community structure is defined as a sub structure in a network that represents connection among users. In this paper, the authors introduced a block modeling method for social structures where nodes have mixed memberships over latent components, and the component interactions generate links. The interactions are grouped in a multinomial style, which allows sparse representations for inference. Two algorithms, which show that the model is able to find the communities and block structures from generated and real data sets, are the concepts of structural equivalence based on Euclidean and the concepts of regular equivalence based on REGE. The summary of the literature survey reflects the two dimensionalities of social networking given below:

Figure 1: Dimensionalities of Social Network

3. Formation of Game Theory Model:

1. Identifying the list of variables involved in Social Networking sites: Twitter and Face book on the
basis of two dimensionalities Graph and Text. e.g.
Graph: Leaders, Followers, Neutrals, Whistleblower, Friend of Friend, Community Detection ….
Text: Rumors, Information propagation, Buffer less Information, Recommendation, Influence
maximization, Immunization, Classification …
2. For formation of Game Theory Model between Twitter and Face book on the basis of graph and
text find the mathematical relationships between these social networking variables by using
predefined mathematical theories.
3. Use of experimental set for Regression Analysis to find dependencies of the entities, in case of
absence of predefined theories e.g. by forming questionnaires and R analytical tool. In view of
Detecting Community or say Friend of friend we can use the concept of CPM/ PERT network
theory to find the source, path and destination of the information propagation.
4. Use of 10-point scale (reflection strong, average, negative relationships) for the uniform
measurement of the coefficients for game theory.
5. Conversion to a LPP (Linear Programming Problem) model for finding most impact variables.
6. Identification and implementation of optimization tool(s) on proposed work.
Proposed Framework: Game theory model for social networking

4. Conclusion:

This research work will provide scientific basis and theoretical support for understanding the global perspective of social networking and nature of cyber crime in social networking sites and suggest ways to prevent it. In view of Graph network, we can identify the source of dispute information as to eliminate or block the links. We can perform sentimental analysis of the Text information as to identify its effect on the society.

5. References:

  1. Hailiang Wang, Yadong Zhouand Xiaohong Guan, “Exploring the Efficiency and Mechanism of Whistleblowing System on Social Networking Site”.
  2. M. Zubair Shafiq, Student Member, IEEE, Muhammad U. Ilyas, Member, IEEE, Alex X. Liu,
    Member, IEEE, and Hayder Radha, Fellow, IEEE “Identifying Leaders and Followers in Online Social Networks.” IEEE journal on selected areas in communication supplement, Vol.31, No.9, September 2013.
  3. Zhaoyan Jin, Quanyuan Wu, Dianxi Shi and Huining Yan, “Random Walk Based Inverse Influence
    Research in Online Social Network” National Key Laboratory for Parallel and Distributed Processing,
    College of Computer, NUDT, Changsha Hunan, P.R.China 410073.
  4. Wenjun Jiang, Jie Wu, and Guojun Wang, “RATE: Recommendation-aware Trust Evaluation in
    Online Social Networks.” 2013 IEEE 12th International Symposium on Network Computing and
  5. Manasvi Talluri, Harneet Kaur, Jing (Selena) He, “Influence Maximization in Social Networks:
    Considering both Positive and Negative Relationships.”
  6. Yang Wei1, Wang Haibo2, Yao Yu3, “An Immunization Strategy for Social Network Worms Based
    on Network Vertex Influence”, China Communications • July 2015.
  7. Mehrnaz Tavan, Roy D. Yates, Waheed U. Bajwa, “Information in Tweets: Analysis of a
    Bufferless Timing Channel Model, 2014 IEEE International Symposium on Information Theory.”
  8. Chenguang Kong, Xiaojun Cao, “Semi-Controlled Authorized Information Dissemination in
    Content-Based Social Networks.” 978-1-4799-3572-7/14/$31.00 ©2014 IEEE.
  9. Sovatana Hour, Li Kan, “Structural and Regular Equivalence of Community Detection in Social Network,” 2014 IEEE/ACM International Conference on Advances in Social Networks Analysis and
    Mining (ASONAM 2014)

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