Generating Random Regular Graphs Quickly

Authors:
A. Steger;N. C. Wormald
Affiliations:
Institut für Informatik, Technische Universität München, D-80290 München, Germany (e-mail: steger@informatik.tu-muenchen.de);Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3052, Australia (e-mail: nick@ms.unimelb.edu.au)
Venue:
Combinatorics, Probability and Computing
Year:
1999

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Abstract

We present a practical algorithm for generating random regular graphs. For all d growing as a small power of n, the d-regular graphs on n vertices are generated approximately uniformly at random, in the sense that all d-regular graphs on n vertices have in the limit the same probability as n → ∞. The expected runtime for these ds is 𝒪(nd2).