1 3 FGSN: Fuzzy Granular Social Networks – Model 4 and applications 5 6 7 Suman Kundu ⇑ , Sankar K. Pal 8 Center for Soft Computing Research, Indian Statistical Institute, Kolkata 700108, India 9 11 article info 12 Article history: 13 Received 16 June 2014 14 Received in revised form 17 March 2015 15 Accepted 29 March 2015 16 Available online xxxx 17 Keywords: 18 Granular computing 19 Fuzzy set 20 Entropy 21 Influence maximization 22 Community detection 23 Big data 24 25 abstract 26 Social network data has been modeled with several approaches, including Sociogram and 27 Sociomatrices, which are popular and comprehensive. Similar to these we have developed 28 here a novel modeling technique based on granular computing theory and fuzzy neighbor- 29 hood systems, which provides a uniform framework to represent social networks. In this 30 model, a social network is represented with a collection of granules. Fuzzy sets are used 31 for defining the granules. The model is named Fuzzy Granular Social Network (FGSN). 32 Familiar measures of networks viz. degree, betweenness, embeddedness and clustering 33 coefficient are redefined in the context of this new framework. Two measures, namely, 34 entropy of FGSN and energy of granules are defined to quantify the uncertainty involved 35 in FGSN arising from fuzziness in the relationships of actors. Experimental results demon- 36 strate the applicability of the model in two well known problems of social networks, 37 namely, target set selection and community detection with comparative studies. 38 Ó 2015 Published by Elsevier Inc. 39 40 41 42 1. Introduction 43 Popularity of on-line social networks like Twitter, Facebook, WhatsApp is increasing day by day. Active presence of the 44 urban society in the e-Universe opens a new avenue of research opportunities. These networks are dynamic, large scale 45 and complex. For a long time, sociologists and economic analysts worked in this field with off-line social network data. 46 But, the data is now available from the on-line social networks which is characterized by large volume, velocity and variety. 47 This forces computer science researchers to come up with new tools and algorithms to analyze these networks effectively 48 and efficiently. 49 Apart from social and economical significance analysis, we can classify the research in social network analysis broadly 50 into four groups namely, (a) analysis of network values [9,19,52], (b) community detection [3,34,4], (c) link predictions 51 [23,26] and (d) evolution of networks [24]. Trivial approach to analyze a network is to model it with graphs and use the net- 52 works analysis tools. Other modeling techniques to work with social network data include, statistical model, sociomatrices 53 model, algebraic model, and agent-based model. There has been a development of game theoretic modeling of the network 54 as well. We will discuss more on these in Section 2. 55 The goal of this paper is to develop a unified framework to model social networks effectively and efficiently. A social net- 56 work is viewed as a collection of relations between social actors and their interactions. These actors form closely operative 57 groups, which are often indistinguishable in the process of problem solving. This resembles the concept of granules. As http://dx.doi.org/10.1016/j.ins.2015.03.065 0020-0255/Ó 2015 Published by Elsevier Inc. ⇑ Corresponding author. E-mail addresses: suman@sumankundu.info (S. Kundu), sankar@isical.ac.in (S.K. Pal). Information Sciences xxx (2015) xxx–xxx Contents lists available at ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins INS 11491 No. of Pages 18, Model 3G 7 April 2015 Please cite this article in press as: S. Kundu, S.K. Pal, FGSN: Fuzzy Granular Social Networks – Model and applications, Inform. Sci. (2015), http://dx.doi.org/10.1016/j.ins.2015.03.065