CCCG: Clique Conversion Ratio Driven Clustering of Graphs

Networks have become ubiquitous in many real world applications and to cluster similar networks is an important problem. There are various properties of graphs such as clustering coefficient (CC), density, arboricity, etc. We introduce a measure, Clique Conversion Coefficient (CCC), which captures the clique forming tendency of nodes in an undirected graph. CCC could either be used as a weighted average of the values in a vector or as the vector itself. Our experiments show that CCC provides additional information about a graph in comparison to related measures like CC and density. We cluster the real world graphs using a combination of the features CCC, CC, and density and show that without CCC as one of the features, graphs with similar clique forming tendencies are not clustered together. The clustering with the use of CCC would have applications in the areas of Social Network Analysis, Protein-Protein Interaction Analysis, etc., where cliques have an important role. We perform the clustering of ego networks of the YOUTUBE network using values in CCC vector as features. The quality of the clustering is analyzed by contrasting the frequent subgraphs in each cluster. The results highlight the utility of CCC in clustering subgraphs of a large graph.