  Communities in social networks or graphs are sets of well-connected,
overlapping vertices. The effectiveness of a community detection algorithm is
determined by accuracy in finding the ground-truth communities and ability to
scale with the size of the data. In this work, we provide three contributions.
First, we show that a popular measure of accuracy known as the F1 score, which
is between 0 and 1, with 1 being perfect detection, has an information lower
bound is 0.5. We provide a trivial algorithm that produces communities with an
F1 score of 0.5 for any graph! Somewhat surprisingly, we find that popular
algorithms such as modularity optimization, BigClam and CESNA have F1 scores
less than 0.5 for the popular IMDB graph. To rectify this, as the second
contribution we propose a generative model for community formation, the
sequential community graph, which is motivated by the formation of social
networks. Third, motivated by our generative model, we propose the
leader-follower algorithm (LFA). We prove that it recovers all communities for
sequential community graphs by establishing a structural result that sequential
community graphs are chordal. For a large number of popular social networks, it
recovers communities with a much higher F1 score than other popular algorithms.
For the IMDB graph, it obtains an F1 score of 0.81. We also propose a
modification to the LFA called the fast leader-follower algorithm (FLFA) which
in addition to being highly accurate, is also fast, with a scaling that is
almost linear in the network size.
