A critical Comparison of Graph Clustering Algorithms Using the K-clique Percolation Technique

In the recent past, various graph clustering algorithms have been proposed. Each algorithm has its own behaviour in terms of performance on a specific data set. So, it is really hard to tell which one is the most efficient and optimal. The concept of k-clique percolation technique in random networks is introduced where k is the size of the complete sub-graphs that are organized into large scale cluster and are analytically and numerically investigated. ErdosRenyi random graph which is undirected and unweighted is choosen for studying the k-clique percolation technique. In an Erdos-Renyi graph with N vertices, where two vertices are connected to each other by an edge with probability pc(k), the percolation transition of kcliques takes place when pc(k) = [(k-1)N] -1/(K-1). Clique percolation has been used in the past for identifying overlapping communities in large real networks. In this paper, restricted neighbourhood search clustering (RNSC) and Markov Clustering (MCL) algorithms are tested in terms of efficiency and optimality using Erdos-Renyi random graphs with varying graph sizes and also using the k-clique percolation technique. The comparison is done between these two algorithms in terms of cluster size and run-time with varying pc (k) according to increasing graph size. To validate the cluster quality obtained by these algorithms, normalized mutual information (NMI) and adjusted mutual information (AMI) are calculated using large scale Erdos-Renyi graph. It is shown that RNSC algorithm is better than MCL using the k-clique percolation technique in terms of cluster size, run-time, NMI and AMI. Keywords— RNSC, MCL, Run-time, Cluster size, NMI, AMI