A generative model for community types in directed networks

TL;DR

This paper introduces a generative model for directed networks that captures all four known community types, including a newly identified source-basin type, and analyzes how model parameters influence community structure.

Contribution

The paper presents a novel generative model for directed networks that reproduces all four community types and provides a mean-field analysis of the conditions leading to each type.

Findings

A difference in swap probabilities leads to core-periphery structure.

A difference in average in-degree leads to source-basin structure.

Multiple transition scenarios between community types are identified.

Abstract

Large complex networks are often organized into groups or communities. In this paper, we introduce and investigate a generative model of network evolution that reproduces all four pairwise community types that exist in directed networks: assortative, core-periphery, disassortative, and the newly introduced source-basin type. We fix the number of nodes and the community membership of each node, allowing node connectivity to change through rewiring mechanisms that depend on the community membership of the involved nodes. We determine the dependence of the community relationship on the model parameters using a mean-field solution. It reveals that a difference in the swap probabilities of the two communities is a necessary condition to obtain a core-periphery relationship and that a difference in the average in-degree of the communities is a necessary condition for a source-basin relationship. More generally, our analysis reveals multiple possible scenarios for the transition between the different structure types, and sheds light on the mechanisms underlying the observation of the different types of communities in network data.