2016/02/17 by Dario Fasino, Fasino, Dario, Francesco Tudisco +1
Computer Science · Materials Science · Physics and Astronomy · #05C50 #15A18 #15B99 #2D Materials and Applications #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Photonic Crystals and Applications #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1602.05457
openalex publication_date 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nodal theorems for generalized modularity matrices ensure that the cluster located by the positive entries of the leading eigenvector of various modularity matrices induces a connected subgraph. In this paper we obtain lower bounds for the modularity of that set of nodes showing that, under certain conditions, the nodal domains induced by eigenvectors corresponding to highly positive eigenvalues of the normalized modularity matrix have indeed positive modularity, that is they can be recognized as modules inside the network. Moreover we establish Cheeger-type inequalities for the cut-modularity of the graph, providing a theoretical support to the common understanding that highly positive eigenvalues of modularity matrices are related with the possibility of subdividing a network into communities.