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Community detection based on strong Nash stable graph partition

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Abstract

The modern science of network mining has brought significant advances to the understanding of complex social networks by studying the modular structures of the networks. The problem of identifying the network modules, also called communities, is an active area of research across several disciplines due to its potential value in real-life applications. The mainstream approach for community detection generally focuses on optimization of a global metric that measures the quality of a partition over a given network. Optimizing a global metric is akin to community assignment by a centralized decision maker. However, communities in a social network often evolve in a decentralized fashion. To model the natural formation of a community, we propose a game theory-based framework treating each node as a player of a hedonic coalition formation game. We propose a novel preference relation for the players based on the players’ preference to form stable and dense community structures. The notion of strong Nash stability is used, for the first time, to determine the outcome of the coalition formation game in the context of community detection. Subsequently, we propose a greedy algorithm to obtain the strong Nash stable partition of the game. Evaluation on the well-known synthetic benchmarks and real-world networks demonstrate the superiority of the proposed algorithm.

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Acknowledgments

The authors express their sincere gratitude to the anonymous reviewers for their valuable suggestions. The suggestions and the comments helped the authors to improve the quality of the manuscript.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Jadavpur University, Kolkata, India

    Srinka Basu & Ujjwal Maulik

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  1. Srinka Basu
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  2. Ujjwal Maulik
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Correspondence to Srinka Basu.

Appendix

Appendix

As modularity (Q) (Newman and Girvan 2004) is a popular goodness metric, its values might be of interest to the readers. However, we exclude the metric from the experiment as otherwise that would make the experiment biased toward the modularity optimization methods like LM. Here, in Table 6 we provide the values of Q for some of the data sets used in the experiment. We also include the modularity of the ground truth partitions where applicable. As shown in the results, LM, which directly optimizes Q, attains maximum Q in all the data sets. It is particularly important to note that the modularity attained by LM is even higher than that of the ground truth partitions, indicating that high modularity does not necessarily indicate a meaningful partition.

Table 6 Modularity values of the partitions
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Basu, S., Maulik, U. Community detection based on strong Nash stable graph partition. Soc. Netw. Anal. Min. 5, 61 (2015). https://doi.org/10.1007/s13278-015-0299-4

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