Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities

TL;DR

This paper introduces new benchmark graphs for testing community detection algorithms on directed, weighted, and overlapping networks, addressing a gap in existing testing methods for complex network structures.

Contribution

It extends previous benchmarks to include direction, weight, and overlapping communities, providing a more realistic testing framework for community detection algorithms.

Findings

Modularity optimization performance on new benchmarks.

Generated graphs with realistic community overlaps.

Benchmark graphs for directed and weighted networks.

Abstract

Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogenous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, like, e. g., social networks. As a practical application, we show how modularity optimization performs on our new benchmark.