Benchmark graphs for testing community detection algorithms

TL;DR

This paper introduces a new class of benchmark graphs that better mimic real network properties for testing community detection algorithms, revealing their limitations more effectively.

Contribution

The authors propose a novel benchmark graph model accounting for heterogeneity in node degrees and community sizes, improving testing of community detection methods.

Findings

New benchmark graphs are more challenging for algorithms.

Standard algorithms show limitations on the new benchmarks.

The new tests reveal previously unnoticed algorithm weaknesses.

Abstract

Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e. the question of how good an algorithm is, with respect to others, is still open. Standard tests include the analysis of simple artificial graphs with a built-in community structure, that the algorithm has to recover. However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks. Here we introduce a new class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this new benchmark to test two popular methods of community detection, modularity optimization and Potts model clustering. The results show that the new benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.