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

TLDR

Complex networks often exhibit community structure—groups of nodes densely connected internally and sparsely connected externally—yet suitable benchmarks for testing community detection, especially for directed and weighted graphs, remain unclear. The authors aim to extend their earlier benchmark framework to produce directed and weighted networks that embed community structure, including overlapping communities. They generate such graphs by assigning heterogeneous node degrees and community sizes, and by permitting nodes to belong to multiple communities. Modularity optimization was evaluated on the new benchmark, demonstrating its performance on directed, weighted, and overlapping community structures.

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 heterogeneous 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, such as social networks. As a practical application, we show how modularity optimization performs on our benchmark.