Generalized modularity matrices
For researchers in network analysis and graph theory, this provides a theoretical foundation for spectral clustering methods, but the contribution is incremental as it synthesizes existing concepts.
The paper unifies various modularity matrices from network analysis and algebraic graph theory, revealing their common spectral properties that underpin community detection algorithms.
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.