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

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Felipe, Lucas Lopes, Avrachenkov, Konstantin, Menasche, Daniel Sadoc
Format: Preprint
Veröffentlicht: 2025
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866914326952017920
author Felipe, Lucas Lopes
Avrachenkov, Konstantin
Menasche, Daniel Sadoc
author_facet Felipe, Lucas Lopes
Avrachenkov, Konstantin
Menasche, Daniel Sadoc
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_03834
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game
Felipe, Lucas Lopes
Avrachenkov, Konstantin
Menasche, Daniel Sadoc
Machine Learning
Artificial Intelligence
Computer Science and Game Theory
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.
title From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game
topic Machine Learning
Artificial Intelligence
Computer Science and Game Theory
url https://arxiv.org/abs/2509.03834