Community Detection in Networks using Graph Distance
This addresses the challenge of community detection with theoretical backing for sparse networks, though it is incremental as it builds on existing block model frameworks.
The authors tackled the problem of community detection in networks by proposing an algorithm based on graph distance, providing theoretical guarantees for block models and extensions to more complex models, with favorable simulation results on datasets like political blogs and Facebook networks.
The study of networks has received increased attention recently not only from the social sciences and statistics but also from physicists, computer scientists and mathematicians. One of the principal problem in networks is community detection. Many algorithms have been proposed for community finding but most of them do not have have theoretical guarantee for sparse networks and networks close to the phase transition boundary proposed by physicists. There are some exceptions but all have some incomplete theoretical basis. Here we propose an algorithm based on the graph distance of vertices in the network. We give theoretical guarantees that our method works in identifying communities for block models and can be extended for degree-corrected block models and block models with the number of communities growing with number of vertices. Despite favorable simulation results, we are not yet able to conclude that our method is satisfactory for worst possible case. We illustrate on a network of political blogs, Facebook networks and some other networks.