NDLI: Decompositions of Triangle-Dense Graphs

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Seshadhri, C. Gupta, Rishi Roughgarden, Tim
Copyright Year	2016
Abstract	High triangle density---the graph property stating that a constant fraction of two-hop paths belongs 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.
Starting Page	197
Ending Page	215
Page Count	19
File Format	PDF
ISSN	00975397
DOI	10.1137/140955331
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2 (Special Section on the Forty-Fifth Annual ACM Symposium on the Theory of Computing (STOC 2013))
Volume Number	45
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-03-01
Access Restriction	Subscribed
Subject Keyword	Social networks clustering Graph algorithms social and information networks graph algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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Decompositions of Triangle-Dense Graphs