Bounds and algorithms for graph trusses
Abstract
The -truss, introduced by Cohen (2005), is a graph where every edge is incident to at least triangles. This is a relaxation of the clique. It has proved to be a useful tool in identifying cohesive subnetworks in a variety of real-world graphs. Despite its simplicity and its utility, the combinatorial and algorithmic aspects of trusses have not been thoroughly explored. We provide nearly-tight bounds on the edge counts of -trusses. We also give two improved algorithms for finding 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 converts a triangle-generation algorithm of Bjorklund et al. (2014) into a dynamic data structure.
Keywords
Cite
@article{arxiv.1806.05523,
title = {Bounds and algorithms for graph trusses},
author = {Paul Burkhardt and Vance Faber and David G. Harris},
journal= {arXiv preprint arXiv:1806.05523},
year = {2023}
}