Network, Popularity and Social Cohesion: A Game-Theoretic Approach

In studies of social dynamics, cohesion refers to a group's tendency to stay in unity, which -- as argued in sociometry — arises from the network topology of interpersonal ties. We follow this idea and propose a game-based model of cohesion that not only relies on the social network, but also reflects individuals' social needs. In particular, our model is a type of cooperative games where players may gain popularity by strategically forming groups. A group is socially cohesive if the grand coalition is core stable. We study social cohesion in some special types of graphs and draw a link between social cohesion and a classical notion of structural cohesion by White and Harary. We then focus on the problem of deciding whether a given social network is socially cohesive and show that this problem is CoNP-complete. Nevertheless, we give two efficient heuristics for coalition structures where players enjoy high popularity and experimentally evaluate their performances.

[1]  Dino Pedreschi,et al.  A classification for community discovery methods in complex networks , 2011, Stat. Anal. Data Min..

[2]  Talal Rahwan,et al.  The Game-Theoretic Interaction Index on Social Networks with Applications to Link Prediction and Community Detection , 2015, IJCAI.

[3]  Wei Chen,et al.  Community Detection in Social Networks through Community Formation Games , 2011, IJCAI.

[4]  Stef Tijs,et al.  Models in Cooperative Game Theory , 2008 .

[5]  Nicholas R. Jennings,et al.  Efficient Computation of the Shapley Value for Game-Theoretic Network Centrality , 2014, J. Artif. Intell. Res..

[6]  L. Moser,et al.  AN EXTREMAL PROBLEM IN GRAPH THEORY , 2001 .

[7]  P. Erdös.  On an extremal problem in graph theory , 1970 .

[8]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[9]  B. Peleg,et al.  Introduction to the Theory of Cooperative Games , 1983 .

[10]  Douglas R. White,et al.  Class, property, and structural endogamy: Visualizing networked histories , 1997 .

[11]  Antonius H. N. Cillessen,et al.  Peer Status in Emerging Adulthood , 2012 .

[12]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[14]  Tomasz P. Michalak,et al.  A Centrality Measure for Networks With Community Structure Based on a Generalization of the Owen Value , 2014, ECAI.

[15]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[16]  N. Gross,et al.  On Group Cohesiveness , 1952, American Journal of Sociology.

[17]  Jeroen Bruggeman,et al.  The social network, socioeconomic background, and school type of adolescent smokers , 2012 .

[18]  Gerrit Müller,et al.  Popularity , 2013, The Journal of Human Resources.

[19]  Michael A. Hogg,et al.  The Social Psychology of Group Cohesiveness: From Attraction to Social Identity , 1992 .

[20]  Kishan G. Mehrotra,et al.  A Game Theoretic Framework for Community Detection , 2012, 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining.

[21]  Albert V. Carron,et al.  Cohesion: Conceptual and Measurement Issues , 2000 .

[22]  D. Lusseau,et al.  The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations , 2003, Behavioral Ecology and Sociobiology.

[23]  S. Fiske,et al.  Social Psychology , 2019, Encyclopedia of Personality and Individual Differences.

[24]  Kishan G. Mehrotra,et al.  Game-Theoretic Framework for Community Detection , 2018, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[25]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[26]  A. Zander,et al.  Group dynamics, research and theory , 1955 .

[27]  Mingxin Zhang,et al.  and Research , 2010 .

[28]  Tomasz P. Michalak,et al.  Efficient Computation of Semivalues for Game-Theoretic Network Centrality , 2015, AAAI.

[29]  F. Harary,et al.  The cohesiveness of blocks in social networks: Node connectivity and conditional density , 2001 .

[30]  Jiamou Liu,et al.  How to Build Your Network? A Structural Analysis , 2016, IJCAI.

[31]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[32]  G. Simmel.  The sociology of Georg Simmel , 1950 .

[33]  Christos Faloutsos,et al.  Graph evolution: Densification and shrinking diameters , 2006, TKDD.

[34]  Mark S. Granovetter.  The Strength of Weak Ties , 1973, American Journal of Sociology.

[35]  Oskar Skibski,et al.  A Shapley Value-based Approach to Determine Gatekeepers in Social Networks with Applications , 2014, ECAI.

[36]  K. Lewin.  Psychology and the Process of Group Living , 1943 .

[37]  Antonius H. N. Cillessen,et al.  Sociometric status and peer group behavior: Previous findings and current directions. , 2004 .