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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).
Chauhan et al. (Tue,) studied this question.