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) .