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Spectral properties of networks with community structure
Sanjeev Chauhan1, Michelle Girvan, Edward Ott
1Department of Physics, University of Maryland, College Park, MD 20742, USA. sanjeevk@umd.edu
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) .
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