On the adjacency matrix of graphs: Principal eigenvector versus degree vector

Abstract

This paper investigates on the relation between the principal eigenvector of the adjacency matrix and the degree vector of a graph. Specifically the analysis deals with the derivation of an upper bound, which only depends on the elements of the matrix, for the difference between the principal eigenvector and the degree vector. The results hold true for a general irreducible, nonnegative, symmetric matrix.