Game Theoretic Clustering for Finding Strong Communities

Author:

Zhao Chao1ORCID,Al-Bashabsheh Ali2,Chan Chung1ORCID

Affiliation:

1. Department of Computer Science, City University of Hong Kong, Hong Kong, China

2. School of General Engineering, Beihang University, Beijing 100191, China

Abstract

We address the challenge of identifying meaningful communities by proposing a model based on convex game theory and a measure of community strength. Many existing community detection methods fail to provide unique solutions, and it remains unclear how the solutions depend on initial conditions. Our approach identifies strong communities with a hierarchical structure, visualizable as a dendrogram, and computable in polynomial time using submodular function minimization. This framework extends beyond graphs to hypergraphs or even polymatroids. In the case when the model is graphical, a more efficient algorithm based on the max-flow min-cut algorithm can be devised. Though not achieving near-linear time complexity, the pursuit of practical algorithms is an intriguing avenue for future research. Our work serves as the foundation, offering an analytical framework that yields unique solutions with clear operational meaning for the communities identified.

Publisher

MDPI AG

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