Metric and spectral properties of dense inhomogeneous random graphs

Abstract

We study metric and spectral properties of dense inhomogeneous random graphs. We generalize results known for the Erdös–Renyi model. In our case an edge(i, j) is present with probability κ(Xi, Xj)p, where κ ≥ 0 is a fixed kernel and Xi are independent variables from a general distribution on a separable metric space.