Determination of Different Sizes of Partitioning Clusters in a Highly Connected Graph

Abstract

Graph representation, even its simplest form, has many applications, ranging from networking to bioinformatics. Graph clustering draws much attentions recently as it enables extraction of useful information, especially when the graph is highly dense. Partitioning Clustering is a popular method in graph clustering. In general, graph clustering is an NP-hard problem, therefore, it is possible to have different forms and different number of clusters with the same density in a highly connected graph. Most research in graph clustering focuses on determining clusters from a specified number of clusters. Nevertheless, knowing different sizes of clusters with similar densities is advantageous with several applications such as validating a service from smaller to larger communities with similar characteristics. This work presents a novel algorithm to determining different sizes of Partitioning Clusters with similar degrees of density in a highly connected graph by using minimum sub-cycles as motifs. The algorithm adopts Greedy-Strategy in partitioning clustering. ‘Intra-Cluster Density’, ‘Difference Density’, ‘Coverage’ and ‘Conductance’ are used as graph clustering metrics.