The Configuration Model for Partially Directed Graphs

TL;DR

This paper introduces a configuration model for partially directed networks, allowing for dependent in-, out-, and undirected degrees, and demonstrates its improved fit to empirical data over existing models.

Contribution

It extends the configuration model to partially directed networks with dependent degrees, providing theoretical convergence conditions and empirical validation.

Findings

Better approximation of empirical networks

Convergence conditions for degree distributions

Model accommodates dependent degrees

Abstract

The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially directed meaning that certain edges are directed and others are undirected. In the paper we define a configuration model for such networks where nodes have in-, out-, and undirected degrees that may be dependent. We prove conditions under which the resulting degree distributions converge to the intended degree distributions. The new model is shown to better approximate several empirical networks compared to undirected and completely directed networks.