The emergence of a giant component in one-dimensional inhomogeneous networks with long-range effects

Abstract

We study the weight-dependent random connection model, a class of sparse graphs featuring many real-world properties such as heavy-tailed degree distributions and clustering. We introduce a coefficient, (deltaf), measuring the effect of the degree-distribution on the occurrence of long edges. We identify a sharp phase transition in (deltaf) for the existence of a giant component in dimension (d=1).