The diameter of Inhomogeneous random graphs

Abstract

In this paper we study the diameter of Inhomogeneous random graphs $G(n,\kappa ,p)$ that are induced by irreducible kernels $\kappa$. The kernels we consider act on separable metric spaces and are almost everywhere continuous. We generalize results known for the Erdős-Rényi model $G(n,p)$ for several ranges of $p$. We find upper and lower bounds for the diameter of $G(n,\kappa ,p)$ in terms of the expansion factor and two explicit constants that depend on the behavior of the kernel over partitions of the metric space.

References in corpus (2)

• A General Formalism for Inhomogeneous Random Graphs
• Critical random graphs: Diameter and mixing time