title: Spectral properties of networks with community structure.
abstract: In this paper, we discuss the eigenspectra of networks with community structure. It is shown that in many cases, the spectrum of eigenvalues of the adjacency matrix of a network with community structure gives a clear indication of the number of communities in the network. In particular, for a network with N nodes and N_(c) communities, there will typically be N_(c) eigenvalues that are significantly larger than the magnitudes of all the other (N-N_(c)) eigenvalues. We discuss this property as well as its use and limitations for determining N_(c) .
authors.affiliation: Department of Physics, University of Maryland, College Park, MD 20742, USA. sanjeevk@umd.edu
authors.forename: Sanjeev
authors.initials: S
authors.lastname: Chauhan
authors.forename: Michelle
authors.initials: M
authors.lastname: Girvan
authors.forename: Edward
authors.initials: E
authors.lastname: Ott
mesh_terms: D000465:Algorithms; D001519:Behavior; D001703:Biophysics / Q000379:methods*; D003142:Communication; D003198:Computer Simulation; D006801:Humans; D020407:Internet; D015233:Models, Statistical; D008962:Models, Theoretical; D011057:Politics