Birth of a strongly connected giant in an inhomogeneous random digraph

TL;DR

This paper introduces a general inhomogeneous random directed graph model with label-dependent arc probabilities and determines the critical point for the emergence of a giant strongly connected component using a branching process approach.

Contribution

It provides a new framework for analyzing inhomogeneous directed graphs and identifies the phase transition point for giant component formation.

Findings

Critical point for giant component emergence identified

Branching process approach applied to directed graphs

Model accommodates label-dependent arc probabilities

Abstract

We present and investigate a general model for inhomogeneous random digraphs with labeled vertices, where the arcs are generated independently, and the probability of inserting an arc depends on the labels of its endpoints and its orientation. For this model the critical point for the emergence of a giant component is determined via a branching process approach.