  To identify communities in directed networks, we propose a generalized form
of modularity in directed networks by introducing a new quantity LinkRank,
which can be considered as the PageRank of links. This generalization is
consistent with the original modularity in undirected networks and the
modularity optimization methods developed for undirected networks can be
directly applied to directed networks by optimizing our new modularity. Also, a
model network, which can be used as a benchmark network in further community
studies, is proposed to verify our method. Our method is supposed to find
communities effectively in citation- or reference-based directed networks.
