  A modularity-specialized label propagation algorithm (LPAm) for detecting
network communities was recently proposed. This promising algorithm offers some
desirable qualities. However, LPAm favors community divisions where all
communities are similar in total degree and thus it is prone to get stuck in
poor local maxima in the modularity space. To escape local maxima, we employ a
multistep greedy agglomerative algorithm (MSG) that can merge multiple pairs of
communities at a time. Combining LPAm and MSG, we propose an advanced
modularity-specialized label propagation algorithm (LPAm+). Experiments show
that LPAm+ successfully detects communities with higher modularity values than
ever reported in two commonly used real-world networks. Moreover, LPAm+ offers
a fair compromise between accuracy and speed.
