Generalized modularity matrices

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.

Please cite this work as:

@article{fasino2016generalized,
  title={Generalized modularity matrices},
  author={Fasino, Dario and Tudisco, Francesco},
  journal={Linear Algebra and its Applications},
  volume={502},
  pages={327--345},
  year={2016},
  publisher={Elsevier}
}

Keywords: Community detection Modularity matrix graph Modularity Nodal domains networks