Eigenvalues and expanders

Noga Alon

doi:10.1007/BF02579166

Eigenvalues and expanders

Noga Alon

Research output: Contribution to journal › Article › peer-review

762 Scopus citations

Abstract

Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander if and only if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian manifolds enables one to generate expanders randomly and check efficiently their expanding properties. It also supplies an efficient algorithm for approximating the expanding properties of a graph. The exact determination of these properties is known to be coNP-complete.

Original language	English
Pages (from-to)	83-96
Number of pages	14
Journal	Combinatorica
Volume	6
Issue number	2
DOIs	https://doi.org/10.1007/BF02579166
State	Published - 1 Jun 1986
Externally published	Yes

Keywords

AMS subject classification (1980): 05C99, 05C50, 68E10

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/BF02579166

Cite this

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AB - Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander if and only if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian manifolds enables one to generate expanders randomly and check efficiently their expanding properties. It also supplies an efficient algorithm for approximating the expanding properties of a graph. The exact determination of these properties is known to be coNP-complete.

KW - AMS subject classification (1980): 05C99, 05C50, 68E10

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Eigenvalues and expanders

Abstract

Keywords

ASJC Scopus subject areas

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