Benchmark graphs for testing community detection algorithms

TLDR

Community structure is a key feature of real networks, yet testing algorithms remains open because existing benchmark graphs do not reflect real node and community properties. The authors introduce a benchmark graph class that incorporates heterogeneous node degree and community size distributions. They propose benchmark graphs with heterogeneous degree and community size distributions and use them to test modularity optimization and Potts model clustering methods. The benchmark reveals greater algorithmic limitations than standard tests, exposing performance limits not evident in initial analyses.

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 class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this benchmark to test two popular methods of community detection, modularity optimization, and Potts model clustering. The results show that the benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.