Network Partitioning Algorithms as Cooperative Games

Abstract: The work is devoted to cooperative and coalitional game-theoretic methods for community detection in networks.The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on coalitional hedonic games. Both approaches allow to detect clusters with various resolutions. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for approaches based on potential hedonic games we suggest a very efficient computational scheme using MCMC Gibbs sampling. This is a joint work with A.Y. Kondratev, V.V. Mazalov and D.G. Rubanov.

Bio: Konstantin Avrachenkov received the master’s degree in control theory from St. Petersburg State Polytechnic University in 1996, the Ph.D. degree in mathematics from the University of South Australia in 2000, and the Habilitation (Doctor of Science) degree from the University of Nice Sophia Antipolis in 2010. Currently, he is Director of Research at Inria Sophia Antipolis, France. His main research interests are Markov processes, singular perturbation theory, optimization, game theory, and analysis of complex networks. He is an Associate Editor of the International Journal of Performance Evaluation, Probability in the Engineering and Informational Sciences and ACM TOMPECS.