Models for Maximization of Spread of Influence in Social Networks

IJSRD - International Journal for Scientific Research & Development| Vol. 4, Issue 04, 2016 | ISSN (online): 2321-0613

Models for Maximization of Spread of Influence in Social Networks Mini Singh Ahuja1 Navpreet Kaur2 1 Assistant Professor 2Student 1,2 GNDU RC-GSP Abstract— Maximize the spread of influence is the fundamental research problem in complex networks. In this we take social network as a graph and motive to find the set of most influential nodes. Influential node means more effective node in the network. The application of this problem is viral marketing in which company have to spread the effect of product by using most popular social websites like Facebook Myspace etc. Various models for maximizing the influence are available [1]. In this paper we learn about the various algorithms and models used for influence maximization.

Key words: Social Networks, Maximum Spread, Cascading I. INTRODUCTION As of late some large scale social network sites for example Facebook, My space and Friendster becomes very effective and successful by giving better results to the users. Also, they are becoming huge due to the maximum influence of spreading. It also leads to word of mouth effect [2].To understand the process of maximization of influence spreading, let us take an example of one small company. It develops a small application for the users and they want to market it through any network. That company has a small amount of budget, so initially they can take a small number of users into network by giving some gifts or any other opportunity [3]. After that, all that users help in spreading of the application by telling friends, family members and so on.

This whole process is done with the word of mouth effect and that application get spreader leads to maximized influence. This type of spreading is used by large companies and also by individual persons for promoting their products and applications [4].

II. RELATED WORK Initially Domingos and Richerdson study about the influence maximization problem by using various algorithms. After that Kempe Klein Berg and Tardos firstly formulate this problem by using various models. Kimura and Saito suggested influence cascade model by using shortest path algorithm to obtain maximum spreading.

Leskovec et al. gives a new technique by using seeds called “Cost Effective Lazy Selecting” scheme also called CELF scheme. Also a new algorithm derived to increase maximization that is the combination of CELF scheme and greedy algorithm and degree discount heuristics are obtained from the independent cascade model and weighted cascade model [5].

III. LINEAR THRESHOLD MODEL this model is proposed by kempe et al. as a reference model to use information in the network. The working of this model is very simple as compared to other models. In this model a whole network is considered as a graph, that graph is directed graph in which G= (V, E). In this V describes the vertices and E describes the edges and relation of individual

nodes. In this model each vertices have two stages. They are active and inactive stage. If one node activated then it does not inactive again, it remains active for all time. Each edge has its own weight, initially the weight is zero. After that diffusion process started in discrete time steps [6]. At first step only one vertex is activated and all the other vertices are inactivated. In second step the other vertices are activated when the weight of the edges increases or it exceeds the threshold value. In extended linear threshold model it allow the vertex activate at positive side or negative side. They can be detected by positive diffusion and negative diffusion. The extended linear model named as competitive linear threshold model. In this model instead of two states it has three states in which each vertex contains inactive +active and –active stage, also each edge of vertex have two weights they are negative weight and positive weight. Once the vertex takes the stage either it is +acive and –active it does not change the stage again. In this two edges occurs one represents the positive influence and another represents the negative influence. While the process starts, at first step it takes two seed sets they are positive seed set and negative seed set. After that in next step both positive and negative influence work independently using the positive and negative thresholds. Those vertices which are activated by positive influence become +active and those which are activate by negative influence they becomes – active vertices. Sometime same vertex contain both positive diffusion and negative diffusion that vertex becomes – active. In this way linear threshold model worked [7].

IV. INDEPENDENT CASCADING MODEL This model is also known as deterministic model. There are two kinds of influence cascades, they are rumours and protectors. There is a graph which contains vertices and edges. Each vertex has three states they are inactive rumours and protected. The active vertex activates all its neighbours.

Rumours and protectors also influence the nodes. They both work at same time, in this each nodes are protected. Every vertex has only one chance to activate their neighbours or influence them. Once the node is activated it will never change its status. The activation of each node by the seed node is done with probability. The nodes have highest probability influence first and so on. In cascading model, there are initial active set of nodes, after that if one edge is activated then it has only one chance to activate another edge (node). If that edge successfully activates another edge, then it is a turn of that activated edge to activate another edge and so on. If it fails to activate the edge then according to the cascading model it do not have any another chance to activate the edges again. It will be come under the category of failed nodes [8].

V. GREEDY ALGORITHM FOR INFLUENCE MAXIMIZATION totalseeds<- 5 seeds <-[25]

All rights reserved by www.ijsrd.com

1123

Models for Maximization of Spread of Influence in Social Networks (IJSRD/Vol. 4/Issue 04/2016/274)

coverednodes<-[25] Repeat for i from 1 to totalseeds-1 iseed=seeds(i) Get children of iseed in array ar. coverednodes=[coverednodes,ar] len=length(ar) Repeat for j from 1 to len el=adjmat(ar(j),:) el(ismember(el,coverednodes))=[ ] count(j)=length(el) endloop [xmax ymax]=max(count) //where ymax is index of maximum value seeds(i+1)=ar(ymax) endloop Above algorithm is used to maximize the spread of influence by taking initial seed nodes. This algorithm takes those nodes which are not influenced by the seed nodes or also those nodes which are failed by the nodes. It finds the maximum children nodes which are not covered under the seed nodes and then put under the covered nodes to influence them [9]. In this way this algorithm increases the effect of nodes and we will get maximum influencing.

VI. HOW TO FIND SEED NODES the most important work of this problem is to find the seed nodes. Seed nodes are those nodes which users have to pick initially for the maximum spreading. So selecting that seed nodes are the most important work of influence maximization problem. In special cases this problem leads to NP-hard problem, in which we have to find the optimal set of seed nodes. For this we have to pick those nodes as seed nodes which have maximum number of children. We also pick those nodes which have maximum neighbours [10]. Maximum the children or maximum neighbours leads to maximum influence of spreading. In this way we can find seed nodes.

SIGKDD international conference on Knowledge discovery and data mining, Pages 199-208, 2009, New York, NY, USA. [4] Zaixin Lu, Wei Zhang et.al. , "Approximation and Inapproximation for The Influence Maximization Problem in Social Networks under Deterministic Linear Threshold Model", 31st International Conference on Distributed Computing Systems Workshops, 2011, pp.

160-165, Minneapolis, MN. [5] Shengfu Zhou, Kun Yue et.al. ,"An Efficient Algorithm for Influence Maximization under Linear Threshold Model", Control and Decision Conference (2014 CCDC), The 26th Chinese, 2014, pp 5352 - 5357, Changsha.

[6] Michalski, R. and Br´odka, P. and Kazienko, P. and Juszczyszyn, K., “Quantifying social network dynamics,” in Proc. of the 4th Conference on Computational Aspects of Social Networks (CASoN), IEEE Computer Society, pp. 69–74, 2012.

[7] Liben-Nowell, D. and Kleinberg, J., “The link prediction problem for social networks,” Journal of the American society for information science and technology, 58, 7, pp. 1019–1031, 2007.

[8] Viswanath, B. and Mislove, A. and Cha, M. and Gummadi, K.P., “On the Evolution of User Interaction in Facebook,” in Proc. Workshop on Online Social Networks, Springer, pp. 37–42, 2009.

[9] Nemenyi, P., “Distribution-free multiple comparisons,” Dissemination at Princeton University, 1963.

[10] Goyal, A. and Bonchi, F. and Lakshmanan, L.V.S., “A data-based approach to social influence maximization,” In Proc. of the VLDB Endowment, 5, 1, pp. 73–84, 2011.

VII. CONCLUSION AND FUTURE WORK In this paper we study about the various models and greedy algorithm used for the influence maximization. This problem is to finding the seed nodes then by the help of those seed nodes activate the inactive nodes by using models and algorithms. In future various modifications are done on greedy algorithm to get maximum influence. Improvements are also done on the working of models [8].

REFERENCES [1] Wei Chen, Yifei Yuan and Li Zhang, "Scalable Influence Maximization in Social Networks under the Linear Threshold Model", ICDM '10 Proceedings of the 2010 IEEE International Conference on Data Mining, Pages 88-97, 2010, Washington, DC, USA. [2] Jankowski, J. and Michalski, R. and Kazienko, P., “Compensatory Seeding in Networks with Varying Availability of Nodes,” in Proc. of 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining ASONAM 2013, pp.

1242–1249, 2013.

[3] Wei Chen, Yajun Wang and SiyuYang,"Efficient Influence Maximization in Social Networks", ACM

All rights reserved by www.ijsrd.com

1124