Eigenvalues and expanders

@article{Alon1986EigenvaluesAE,
  title={Eigenvalues and expanders},
  author={Noga Alon},
  journal={Combinatorica},
  year={1986},
  volume={6},
  pages={83-96}
}
  • N. Alon
  • Published 2 January 1986
  • Computer Science, Mathematics
  • Combinatorica
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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The method of taking the sample average from one trajectory is a more efficient estimate of /spl pi/(A) than the standard method of generating independent sample points from several trajectories and improves the algorithms of Jerrum and Sinclair (1989) for approximating the number of perfect matchings in a dense graph.
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