A Statistical Test of Heterogeneous Subgraph Densities to Assess Clusterability

Abstract

Determining if a graph displays a clustered structure prior to subjecting it to any cluster detection technique has recently gained attention in the literature. Attempts to group graph vertices into clusters when a graph does not have a clustered structure is not only a waste of time but will also lead to misleading conclusions. To address this problem, we introduce a novel statistical test, the δ-test, which is based on comparisons of local and global densities. Our goal is to assess whether a given graph meets the necessary conditions to be meaningfully summarized by clusters of vertices. We empirically explore our test's behavior under a number of graph structures. We also compare it to other recently published tests. From a theoretical standpoint, our test is more general, versatile and transparent than recently published competing techniques. It is based on the examination of intuitive quantities, applies equally to weighted and unweighted graphs and allows comparisons across graphs. More importantly, it does not rely on any distributional assumptions, other than the universally accepted definition of a clustered graph. Empirically, our test is shown to be more responsive to graph structure than other competing tests.

Using Synthetic Networks for Parameter Tuning in Community Detection

“…We will further make similar observations for other algorithms on this dataset. Such instability may mean that this dataset does not have a clear community structure (which can sometimes be the case for real-world networks [18]).…”

Graph Clustering Via QUBO and Digital Annealing

“…For example, clusters are arguably uninformative in the case of complete graphs. In fact, the topic of clusterability, the assessment of a graph's suitability to a clustering exercise, has received some attention in the recent literature [15,16,5,28]. For the purpose of this article, we restrict our attention to clusterable, undirected, unweighted and weighted graphs, with no self loops or multiple edges.…”