Spectral Radius of Graphs

Abstract

Graphs are naturally associated with matrices, as matrices provide a simple way of representing graphs in computer memory. The basic one of these is the adjacency matrix, which encodes existence of edges joining vertices of a graph. Knowledge of spectral properties of the adjacency matrix is often useful to describe graph properties which are related to the density of the graph’s edges, on either a global or a local level. For example, entries of the principal eigenvector of adjacency matrices have been used in the study of complex networks, introduced under the name eigenvector centrality by the renowned mathematical sociologist Phillip Bonacich back in 1972; see [5, 6].