Line Graphs of Weighted Networks for Overlapping Communities

摘要

In this paper, we develop the idea to partition the edges of a weighted graphin order to uncover overlapping communities of its nodes. Our approach is basedon the construction of different types of weighted line graphs, i.e. graphswhose nodes are the links of the original graph, that encapsulate differentlythe relations between the edges. Weighted line graphs are argued to provide analternative, valuable representation of the system's topology, and are shown tohave important applications in community detection, as the usual node partitionof a line graph naturally leads to an edge partition of the original graph.This identification allows us to use traditional partitioning methods in orderto address the long-standing problem of the detection of overlappingcommunities. We apply it to the analysis of different social and geographicalnetworks.