On a general class of inhomogeneous random digraphs

TL;DR

This paper introduces a broad class of inhomogeneous directed random graphs, analyzing their phase transitions, degree distributions, and how to generate scale-free graphs with arbitrary degree dependence.

Contribution

It generalizes existing models by including various special cases and provides theoretical results on phase transitions and degree distributions.

Findings

Established phase transition for giant strongly connected component

Derived limiting joint degree distribution

Showed how to generate scale-free graphs with arbitrary degree dependence

Abstract

We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models includes as special cases the directed versions of the Erdos-Renyi model, graphs with given expected degrees, the generalized random graph, and the Poissonian random graph. We establish the phase transition for the existence of a giant strongly connected component and provide some other basic properties, including the limiting joint distribution of the degrees and the mean number of arcs. In particular, we show that by choosing the joint distribution of the vertex attributes according to a multivariate regularly varying distribution, one can obtain scale-free graphs with arbitrary in-degree/out-degree dependence.