Partitioning Graph Clustering With User-Specified Density

Graph clustering has attracted many interests in recent years, with numerous applications ranging from the clustering of computer networks to the detection of social communities. It presents a challenging NP-class problem, and as a result, numerous algorithms have been developed, each tailored to specific objectives and quality metrics for evaluation. This research commences by categorizing existing graph clustering algorithms based on two distinct perspectives: parameter-free algorithms and user-defined or adjustable parametric algorithms. Quality metrics are further categorized into three distinct groups: internal connectivity, external connectivity, and a combination of both. If a task can be represented by a simple undirected and unweighted graph, from a management and deployment of resources perspective, having clusters of some kind of similar density is advantageous as it allows efficient management. This research introduces a partitioning graph clustering algorithm that allows users to specify the desired density of a cluster by means of 'relative density'. Clustering process involves the determination of all triangles (i.e., smallest cliques) and selecting a clique as an initial cluster. The expansion of a cluster is done by adding adjacent cliques while the required relative density is monitored. Existing metrics are found unsuitable for evaluating the proposed method; therefore, a suitable new metric, the Mean Relative Density Deviation Coefficient (MRDDC), is introduced.