Local structure of directed networks

TL;DR

This paper investigates the local structure of directed networks, revealing that real directed networks often have fewer short loops than random models, with a new theory to compare loop densities.

Contribution

It introduces a novel theoretical framework for analyzing the local loop structure of directed networks and compares real networks to randomized models.

Findings

Real directed networks have fewer short loops than random models.

Developed conditions to determine loop density differences.

Implications for dynamics and structure of directed networks.

Abstract

Previous work on undirected small-world networks established the paradigm that locally structured networks tend to have high density of short loops. On the other hand, many realistic networks are directed. Here we investigate the local organization of directed networks and find, surprisingly, that real networks often have very few short loops as compared to random models. We develop a theory and derive conditions for determining if a given network has more or less loops than its randomized counterpart. These findings carry broad implications for structural and dynamical processes sustained by directed networks.