On Cheeger-type inequalities for weighted graphs

  • Authors:

  • Shmuel Friedland;Reinhard Nabben

  • Affiliations:

  • Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607-7045;Fakultät für Mathematik, Universität Bielefeld, Postfah 100131, 33501 Bielefeld, Germany

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2002

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Abstract

We give several bounds on the second smallest eigenvalue of the weighted Laplacian matrix of a finite graph and on the second largest eigenvalue of its weighted adjacency matrix. We establish relations between the given Cheeger-type bounds here and the known bounds in the literature. We show that one of our bounds is the best Cheeger-type bound available. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 1–17, 2002