Community detection and unveiling of hierarchy in networks: a density-based clustering approach

The unveiling of communities within a network or graph, and the hierarchization of its members that results is of utmost importance in areas ranging from social to biochemical networks, from electronic circuits to cybersecurity. We present a statistical mechanics approach that uses a normalized Gaussian function which captures the impact of a node within its neighborhood and leads to a density-ranking of nodes by considering the distance between nodes as punishment. A hill-climbing procedure is applied to determine the density attractors and identify the unique parent (leader) of each member as well as the group leader. This organization of the nodes results in a tree-like network with multiple clusters, the community tree. The method is tested using synthetic networks generated by the LFR benchmarking algorithm for network sizes between 500 and 30,000 nodes and mixing parameter between 0.1 and 0.9. Our results show a reasonable agreement with the LFR results for low to medium values of the mixing parameter and indicate a very mild dependence on the size of the network.