Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphs

Abstract

A Chung–Lu random graph is an inhomogeneous Erdős–Rényi random graph in which vertices are assigned average degrees, and pairs of vertices are connected by an edge with a probability that is proportional to the product of their average degrees, independently for different edges. We derive a central limit theorem for the principal eigenvalue and the components of the principal eigenvector of the adjacency matrix of a Chung–Lu random graph. Our derivation requires certain assumptions on the average degrees that guarantee connectivity, sparsity and bounded inhomogeneity of the graph.

Keywords

• Chung–Lu random graph
• adjacency matrix
• principal eigenvalue and eigenvector
• central limit theorem