A Framework for Community Detection in Large Networks Using Game-Theoretic Modeling

Community detection is a fundamental component of large network analysis. In both academia and industry, progressive research has been made on problems related to community network analysis. Community detection is gaining significant attention and importance in the area of network science. Regular and synthetic complex networks have motivated intense interest in studying the fundamental unifying principles of various complex networks. This paper presents a new game-theoretic approach towards community detection in large-scale complex networks based on modified modularity; this method was developed based on modified adjacency, modified Laplacian matrices and neighborhood similarity. This approach was used to partition a given network into dense communities. It is based on determining a Nash stable partition, which is a pure strategy Nash equilibrium of an appropriately defined strategic game in which the nodes of the network were the players and the strategy of a node was to decide to which community it ought to belong. Players chose to belong to a community according to a maximized fitness/payoff. Quality of the community networks was assessed using modified modularity along with a new fitness function. Community partitioning was performed using Normalized Mutual Information and a ‘modularity measure’, which involved comparing the new game-theoretic community detection algorithm (NGTCDA) with well-studied and well-known algorithms, such as Fast Newman, Fast Modularity Detection, and Louvain Community. The quality of a network partition in communities was evaluated by looking at the contribution of each node and its neighbors against the strength of its community.

[1]  Zhi-Ping Liu,et al.  Identifying overlapping communities in social networks using multi-scale local information expansion , 2012, The European Physical Journal B.

[2]  Ulrik Brandes,et al.  On Finding Graph Clusterings with Maximum Modularity , 2007, WG.

[3]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[4]  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.

[5]  Andreas Geyer-Schulz,et al.  The Randomized Greedy Modularity Clustering Algorithm and the Core Groups Graph Clustering Scheme , 2014 .

[6]  P. Morris.  Introduction to Game Theory , 1994 .

[7]  Pravin Chopade,et al.  Community Detection in Large Scale Big Data Networks , 2014 .

[8]  Nitesh V. Chawla,et al.  Identifying and evaluating community structure in complex networks , 2010, Pattern Recognit. Lett..

[9]  Yung-Ming Li,et al.  Knowledge sharing in communities of practice: A game theoretic analysis , 2010, Eur. J. Oper. Res..

[10]  Andrea Lancichinetti,et al.  Detecting the overlapping and hierarchical community structure in complex networks , 2008, 0802.1218.

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

[12]  R. McKelvey,et al.  Computation of equilibria in finite games , 1996 .

[13]  Boleslaw K. Szymanski,et al.  Overlapping community detection in networks: The state-of-the-art and comparative study , 2011, CSUR.

[14]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Claudio Castellano,et al.  Defining and identifying communities in networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Hamidreza Alvari,et al.  Discovering overlapping communities in social networks: A novel game-theoretic approach , 2013, AI Commun..

[17]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .

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

[19]  Hamidreza Alvari,et al.  Community detection in dynamic social networks: A game-theoretic approach , 2014, 2014 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2014).

[20]  S. Fortunato,et al.  Resolution limit in community detection , 2006, Proceedings of the National Academy of Sciences.

[21]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Justin Zhan,et al.  Node attributes and edge structure for large-scale big data network analytics and community detection , 2015, 2015 IEEE International Symposium on Technologies for Homeland Security (HST).

[23]  Marwan Bikdash,et al.  New centrality measures for assessing smart grid vulnerabilities and predicting brownouts and blackouts , 2016, Int. J. Crit. Infrastructure Prot..

[24]  Santo Fortunato,et al.  Limits of modularity maximization in community detection , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[26]  Bapi Chatterjee,et al.  An optimization formulation to compute Nash equilibrium in finite games , 2009, 2009 Proceeding of International Conference on Methods and Models in Computer Science (ICM2CS).

[27]  Justin Zhijun Zhan,et al.  Structural and functional analytics for community detection in large-scale complex networks , 2015, Journal of Big Data.

[28]  Marwan Bikdash,et al.  Robustness and survivability of smart power grid and scada networks when subjected to severe emergencies, vulnerability and wmd attacks , 2013 .

[29]  M. Newman.  Communities, modules and large-scale structure in networks , 2011, Nature Physics.

[30]  Anca Andreica,et al.  Game Theory and Extremal Optimization for Community Detection in Complex Dynamic Networks , 2014, PloS one.

[31]  Y. Narahari,et al.  A game theory inspired, decentralized, local information based algorithm for community detection in social graphs , 2012, Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012).

[32]  Wei Chen,et al.  A game-theoretic framework to identify overlapping communities in social networks , 2010, Data Mining and Knowledge Discovery.

[33]  Peter F. Stadler,et al.  Laplacian Eigenvectors of Graphs , 2007 .

[34]  Jure Leskovec,et al.  Discovering social circles in ego networks , 2012, ACM Trans. Knowl. Discov. Data.

[35]  Rodica Ioana Lung,et al.  A Game Theoretic Approach to Community Detection in Social Networks , 2011, NICSO.

[36]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Clara Pizzuti,et al.  Overlapped community detection in complex networks , 2009, GECCO.

[38]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Bruce Bueno de Mesquita,et al.  An Introduction to Game Theory , 2014 .

[40]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.