Map equation for link community
  Community structure exists in many real-world networks and has been reported being related to several functional properties of the networks. The conventional approach was partitioning nodes into communities, while some recent studies start partitioning links instead of nodes to find overlapping communities of nodes efficiently. We extended the map equation method, which was originally developed for node communities, to find link communities in networks. This method is tested on various kinds of networks and compared with the metadata of the networks, and the results show that our method can identify the overlapping role of nodes effectively. The advantage of this method is that the node community scheme and link community scheme can be compared quantitatively by measuring the unknown information left in the networks besides the community structure. It can be used to decide quantitatively whether or not the link community scheme should be used instead of the node community scheme. Furthermore, this method can be easily extended to the directed and weighted networks since it is based on the random walk. 
Youngdo Kim, Hawoong Jeong
physics.soc-ph cond-mat.stat-mech cs.SI