Models and average properties of scale-free directed networks

TL;DR

This paper extends a merging model to directed networks, revealing two distinct types with features similar to biological networks, and introduces measures to distinguish these network types and their properties.

Contribution

It introduces two new directed network models, analyzes their properties, and compares them to biological networks, highlighting their similarities and differences.

Findings

Two types of directed networks emerge: friendly and hostile merging.

Features of these networks resemble metabolic and transcriptional networks.

Measures can distinguish between the two network types and identify unique features.

Abstract

We extend the merging model for undirected networks by Kim et al. [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile merging, give rise to two distinct network types. We uncover that some non-trivial features of these two network types resemble two levels of a certain randomization/non-specificity in the link reshuffling during network evolution. Furthermore the same features show up, respectively, in metabolic networks and transcriptional networks. We introduce measures that single out the distinguishing features between the two prototype networks, as well as point out features which are beyond the prototypes.