Bounds and algorithms for k-truss
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A k-truss is a relaxation of a k-clique developed by Cohen (2005), specifically a connected graph in which every edge is incident to at least k triangles. The k-truss has proved to be a useful tool in identifying cohesive networks in real-world graphs such as social networks. Despite its simplicity and its utility, the combinatorial and algorithmic aspects of k-truss have not been thoroughly explored. We provide nearly-tight bounds on the edge counts of k-trusses. We also give two improved algorithms for finding k-trusses in large-scale graphs. First, we present a simplified and faster algorithm, based on approach discussed in Wang & Cheng (2012). Second, we present a theoretical algorithm based on fast matrix multiplication; this extends an algorithm of Bjorklund et al. (2014) for generating triangles from a static graph to a dynamic data-structure.
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