Benchmark graphs for the evaluation of clustering algorithms

Artificial graphs are commonly used for the evaluation of community mining and clustering algorithms. Each artificial graph is assigned a pre-specified clustering, which is compared to clustering solutions obtained by the algorithms under evaluation. Hence, the pre-specified clustering should comply with specifications that are assumed to delimit a good clustering. However, existing construction processes for artificial graphs do not set explicit specifications for the pre-specified clustering. We call these graphs, randomly clustered graphs. Here, we introduce a new class of benchmark graphs which are clustered according to explicit specifications. We call them optimally clustered graphs. We present the basic properties of optimally clustered graphs and propose algorithms for their construction. Experimentally, we compare two community mining algorithms using both randomly and optimally clustered graphs. Results of this evaluation reveal interesting insights both for the algorithms and the artificial graphs.