Generalized modularity matrices

TL;DR

This paper explores the common traits and spectral properties of various modularity matrices used in network analysis and graph clustering, providing insights into their theoretical foundations and practical applications.

Contribution

It identifies shared characteristics of modularity matrices and analyzes their spectral properties, enhancing understanding of their role in community detection algorithms.

Findings

Identifies common traits among different modularity matrices

Analyzes spectral properties relevant to graph clustering

Provides theoretical insights supporting community detection methods

Abstract

Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral-type algorithms for community detection.