Discovering Communities through Friendship

We introduce a new method for detecting communities of arbitrary size in an undirected weighted network. Our approach is based on tracing the path of closest-friendship between nodes in the network using the recently proposed Generalized Erds Numbers. This method does not require the choice of any arbitrary parameters or null models, and does not suffer from a system-size resolution limit. Our closest-friend community detection is able to accurately reconstruct the true network structure for a large number of real world and artificial benchmarks, and can be adapted to study the multi-level structure of hierarchical communities as well. We also use the closeness between nodes to develop a degree of robustness for each node, which can assess how robustly that node is assigned to its community. To test the efficacy of these methods, we deploy them on a variety of well known benchmarks, a hierarchal structured artificial benchmark with a known community and robustness structure, as well as real-world networks of coauthorships between the faculty at a major university and the network of citations of articles published in Physical Review. In all cases, microcommunities, hierarchy of the communities, and variable node robustness are all observed, providing insights into the structure of the network.