17 Spectral properties, transport, diffusion and dynamics
In this chapter we discuss the spectral properties of networks, and their relation to dynamical properties such as diffusion. There are two main characteristic matrices for a graph, the adjacency matrix and the Laplacian. We discuss both of them and explain the relation to the dynamical properties. A good summary of results on the spectrum of networks can be found in [Chu97]. For a nice survey of random walks on graphs see [Lov96].
17.1 The spectrum of the adjacency matrix
As described in Chapter 1, the adjacency matrix, A, is an N× N matrix (where N is the number of nodes) whose entries ...