Decompositions of triangle-dense graphs

Authors:
Rishi Gupta;Tim Roughgarden;C. Seshadhri
Affiliations:
Stanford University, Stanford, CA, USA;Stanford University, Stanford, CA, USA;Sandia National Laboratories, Livermore, CA, USA
Venue:
Proceedings of the 5th conference on Innovations in theoretical computer science
Year:
2014

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Abstract

High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove constructively that significant portions of a triangle-dense graph are contained in a disjoint union of dense, radius 2 subgraphs. This result quantifies the extent to which triangle-dense graphs resemble unions of cliques. We also show that our algorithm recovers planted clusterings in approximation-stable k-median instances.