EIGENVALUES AND EXPANDERS

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EIGENVALUES AND EXPANDERS (1986)

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by N. Alon

Venue:	COMBINATORICA
Citations:	400 - 20 self

BibTeX

@MISC{Alon86eigenvaluesand,
    author = {N. Alon},
    title = { EIGENVALUES AND EXPANDERS},
    year = {1986}
}

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Abstract

Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly 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.

Keyphrases

eigenvalue expanders expanding property riemannian manifold efficient algorithm numerous application exact determination analytic analogue linear expanders adjacency matrix regular bipartite graph theoretical computer science

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