We propose to partition the edges of a graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the edges of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs provide an alternative, valuable representation of the system's topology, and have important applications in community detection, as the usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities.
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