Comparing Game-Theoretic and Maximum Likelihood Approaches for Network Partitioning
The purpose of this article is to show the relationship between the game-theoretic approach and the maximum likelihood method in the problem of community detection in networks. We formulate a cooperative game related with network structure where the nodes are players in a hedonic game and then we find the stable partition of the network into coalitions. This approach corresponds to the problem of maximizing a potential function and allows to detect clusters with various resolution. We propose here the maximum likelihood method for the tuning of the resolution parameter in the hedonic game. We illustrate this approach by some numerical examples.
KeywordsNetwork partitioning Community detection Cooperative games Hedonic games Tuning of the parameter Maximum likelihood method
This research is supported by the Russian Fund for Basic Research (projects 16-51-55006, 16-01-00183) and Shandong Province “Double-Hundred Talent Plan (No. WST2017009)”.
- 1.Avrachenkov, K., Dobrynin, V., Nemirovsky, D., Pham, S.K., Smirnova, E.: Pagerank based clustering of hypertext document collections. Proc. ACM SIGIR 2008, 873–874 (2008)Google Scholar
- 2.Avrachenkov, K., El Chamie, M., Neglia, G.: Graph clustering based on mixing time of random walks. Proc. IEEE ICC 2014, 4089–4094 (2014)Google Scholar
- 4.Blatt, M., Wiseman, S., Domany, E.: Clustering data through an analogy to the Potts model. In: Proceedings of NIPS 1996, pp. 416–422 (1996)Google Scholar
- 7.Copic, J., Jackson, M., Kirman, A.: Identifying community structures from network data via maximum likelihood methods. B.E. J. Theor. Econ. 9(1) (2009). 1935-1704Google Scholar
- 8.Dongen, S.: Performance criteria for graph clustering and Markov cluster experiments, CWI Technical report (2000)Google Scholar
- 14.Meila, M., Shi, J.: A random walks view of spectral segmentation. In: Proceedings of AISTATS (2001)Google Scholar
- 15.Newman, M.E.J.: Modularity and community structure in networks. Soc. Netw. 103(23), 8577–8582 (2006)Google Scholar