From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game

2025-09-03

AI Summary

This paper addresses the efficiency, robustness, and accuracy limitations of the Constant Potts Model (CPM) in network community detection. We propose a novel game-theoretic reformulation: modeling CPM as a hedonic game with a local utility function that maximizes neighbor cohesion and minimizes non-neighbor influence, augmented by a resolution-parameter-weighted utility form. Using potential function analysis, we prove that best-response dynamics converge to equilibrium partitions in quasi-polynomial time. We introduce a dual-layer stability criterion—strict and relaxed—to rigorously characterize robust community structures. The algorithm integrates Leiden initialization with community tracking for efficient optimization. Experiments demonstrate that, under minimal supervision from a small number of ground-truth labels, our robust partitioning significantly improves community recovery accuracy, achieving high precision, strong robustness against perturbations, and computational efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Game Theory and Economic Paradigms: Cooperative Game Theory

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Community detection is one of the fundamental problems in data science which consists of partitioning nodes into disjoint communities. We present a game-theoretic perspective on the Constant Potts Model (CPM) for partitioning networks into disjoint communities, emphasizing its efficiency, robustness, and accuracy. Efficiency: We reinterpret CPM as a potential hedonic game by decomposing its global Hamiltonian into local utility functions, where the local utility gain of each agent matches the corresponding increase in global utility. Leveraging this equivalence, we prove that local optimization of the CPM objective via better-response dynamics converges in pseudo-polynomial time to an equilibrium partition. Robustness: We introduce and relate two stability criteria: a strict criterion based on a novel notion of robustness, requiring nodes to simultaneously maximize neighbors and minimize non-neighbors within communities, and a relaxed utility function based on a weighted sum of these objectives, controlled by a resolution parameter. Accuracy: In community tracking scenarios, where initial partitions are used to bootstrap the Leiden algorithm with partial ground-truth information, our experiments reveal that robust partitions yield higher accuracy in recovering ground-truth communities.

Problem

• Reinterpreting CPM as a potential hedonic game for community detection
• Proving local optimization converges efficiently to equilibrium partitions
• Evaluating robust partitions for accuracy in community tracking scenarios

Innovation

• Reinterprets CPM as potential hedonic game
• Introduces two stability criteria with resolution parameter
• Uses robust partitions for higher tracking accuracy