Community detection in directed acyclic graphs

TL;DR

This paper introduces a new modularity measure tailored for community detection in directed acyclic graphs (DAGs), such as citation networks, and demonstrates its effectiveness through spectral methods and empirical testing.

Contribution

The paper proposes a novel modularity for DAGs that respects node order, along with a spectral method to optimize it, improving community detection in temporal networks.

Findings

Modularity values for DAGs are similar to those for undirected and general directed networks.

Maximizing conventional modularity in DAGs yields partitions close to the DAG-specific optimal.

The spectral method effectively approximates the maximization of the proposed DAG modularity.

Abstract

Some temporal networks, most notably citation networks, are naturally represented as directed acyclic graphs (DAGs). To detect communities in DAGs, we propose a modularity for DAGs by defining an appropriate null model (i.e., randomized network) respecting the order of nodes. We implement a spectral method to approximately maximize the proposed modularity measure and test the method on citation networks and other DAGs. We find that the attained values of the modularity for DAGs are similar for partitions that we obtain by maximizing the proposed modularity (designed for DAGs), the modularity for undirected networks and that for general directed networks. In other words, if we neglect the order imposed on nodes (and the direction of links) in a given DAG and maximize the conventional modularity measure, the obtained partition is close to the optimal one in the sense of the modularity for DAGs.