Abstract
In real world complex networks, communities are usually both overlapping and hierarchical. A very important class of complex networks is the bipartite networks. Maximal bicliques are the strongest possible structural communities within them.Here we consider overlapping communities in bipartite networks and propose a method that detects an order-limited number of overlapping maximal bicliques covering the network. We formalise a measure of relative community strength by which communities can be categorised, compared and ranked. There are very few real bipartite datasets for which any external ground truth about overlapping communities is known. Here we test three such datasets. We categorise and rank the maximal biclique communities found by our algorithm according to our measure of strength. Deeper analysis of these bicliques shows they accord with ground truth and give useful additional insight. Based on this we suggest our algorithm can find true communities at the first level of a hierarchy. We add a heuristic merging stage to the maximal biclique algorithm to produce a second level hierarchy with fewer communities and obtain positive results when compared with other overlapping community detection algorithms for bipartite networks.
Highlights
The main contribution of this paper is an algorithm combining three concepts that can improve community detection in bipartite networks
In order to evaluate our algorithm we have examined in detail three real bipartite social networks for which some external ground truth information or metadata analysis about communities in either set P, or set S, is available
Because there is no ground truth published for overlapping communities in the whole network and we have demonstrated that our communities well represent the ground truth, we make the assumption that the strongest structural communities are a true base level of the hierarchical overlapping community structure of this network
Summary
The main contribution of this paper is an algorithm combining three concepts (node similarity, maximal bicliques and cliques) that can improve community detection in bipartite networks. The algorithm we introduce, MaxBic, produces overlapping maximal bicliques, covers the network and forms the base level of a community hierarchy. These bicliques are as tightly connected internally as is possible in the network. MaxBic is a deterministic algorithm and requires no predefined parameters such as the number of communities, maximum number of community memberships, or allowed proportion of overlap, as initial input. For a network with n nodes, it produces no more than n maximal bicliques. We show its time complexity is at worst O n3 , irrespective of whether the network is dense or sparse
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