Diclique clustering in a directed random graph

TL;DR

This paper introduces a new clustering concept for directed graphs based on dicliques, supported by a two-mode model that explains their structural properties and degree distributions.

Contribution

It presents a novel clustering notion for directed graphs and a two-mode model explaining diclique formation and degree distributions.

Findings

Directed graphs exhibit nontrivial clustering with dicliques.

The two-mode model captures power-law degree distributions.

Dicliques are key structural components in real-world networks.

Abstract

We discuss a notion of clustering for directed graphs, which describes how likely two followers of a node are to follow a common target. The associated network motifs, called dicliques or bi-fans, have been found to be key structural components in various real-world networks. We introduce a two-mode statistical network model consisting of actors and auxiliary attributes, where an actor i decides to follow an actor j whenever i demands an attribute supplied by j. We show that the digraph admits nontrivial clustering properties of the aforementioned type, as well as power-law indegree and outdegree distributions.