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Laplacians and the Cheeger Inequality for Directed Graphs

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Abstract.

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of non-reversible Markov chains including bounding the rate of convergence and deriving comparison theorems.

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  1. University of California, San Diego, La Jolla, CA, 92093-0112, USA

    Fan Chung

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  1. Fan Chung
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Correspondence to Fan Chung.

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Received September 8, 2004

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Chung, F. Laplacians and the Cheeger Inequality for Directed Graphs. Ann. Comb. 9, 1–19 (2005). https://doi.org/10.1007/s00026-005-0237-z

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  • DOI: https://doi.org/10.1007/s00026-005-0237-z

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