Work

Decompositions of Triangle-Dense Graphs

Year: 2013

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1309.7440

Authors: Gupta, Rishi, Roughgarden, Tim, Seshadhri, C.

Institutions: Stanford University, Sandia National Laboratories California, Sandia National Laboratories

Language: English

Topic: Complex Network Analysis Techniques

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, National Nuclear Security Administration, Multidisciplinary University Research Initiative, Office of Naval Research, Air Force Office of Scientific Research, Sandia National Laboratories

Awards: G1626522811, G194215011, G2075401295, G3469581542, G351415096, AF: Small: Frontiers in Algorithmic Game Theory, G6485281451, ICES: Small: Frontiers in Mechanism Design, G7318852158, G8456466421

OpenAlex ID: W2953265488

Cites: 37

Cited by: 2

Related to: 10