# Eigenvalues and expanders

@article{Alon1986EigenvaluesAE, title={Eigenvalues and expanders}, author={Noga Alon}, journal={Combinatorica}, year={1986}, volume={6}, pages={83-96} }

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

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