  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.
