Complex Networks: A Networking and Signal Processing Perspective

Chapter 8Spectra of Complex Networks

The eigenvalues and eigenvectors of a structure matrix of a complex network reveal information about its topology and its collective behavior. These structure matrices can be the adjacency matrix, weight matrix, Laplacian matrix, or random walk matrix of the graph representing a complex network. Studying the spectra, that is, the eigendecomposition of these matrices, leads to interesting results about the underlying network. For example, eigendecomposition of the Laplacian matrix helps in identifying communities (clusters) in a social network. Moreover, spectral densities of various complex network models follow specific patterns and, therefore, allow classification of networks. Furthermore, the eigenvalues ...