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A great deal of community detection communities is based on the maximization of the measure known as modularity. There is a dearth of literature on overlapping community detection algorithms, in spite of the importance of the applications and the overwhelming number of community detection algorithms yet proposed. To this end, one of the suggestions in the literature consists of partitioning the set of edges into communities, also known as link partitions, by applying community detection algorithms to line graphs. In line with this, in this paper, overlapping vertex communities are obtained from link partitions by a method that selects the communities of the edges that represent the highest modularity gain. We also introduce a spectral algorithm to find link partitions from line graphs. We show that the modularity of communities in line graphs is equivalent to the adaptation of modularity of communities in the original graphs, when considering the non-backtracking matrix instead of the adjacency matrix in its formula. The results of the experiments carried out with overlapping community detection algorithms showed that the proposed method is competitive with state-of-the-art algorithms.

Spectral Algorithm for Line Graphs to Find Overlapping Communities in Social Networks