Szemerédi's regularity lemma for sparse graphs
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
On triangle-free random graphs
Random Structures & Algorithms
Szemerédi-type clustering of peer-to-peer streaming system
Proceedings of the 2011 International Workshop on Modeling, Analysis, and Control of Complex Networks
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Szemerédi's Regularity Lemma is an important tool for analysing the structure of dense graphs. There are versions of the Regularity Lemma for sparse graphs, but these only apply when the graph satisfies some local density condition. In this paper, we prove a sparse Regularity Lemma that holds for all graphs. More generally, we give a Regularity Lemma that holds for arbitrary real matrices.