Fast uniform generation of regular graphs
Theoretical Computer Science
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
Random Structures & Algorithms
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Constructing and sampling graphs with a prescribed joint degree distribution
Journal of Experimental Algorithmics (JEA)
Exact and efficient generation of geometric random variates and random graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of steps to run such a chain, so that we generate truly independent samples. Theoretical bounds for mixing times of these Markov chains are too large to be practically useful. Practitioners have no useful guide for choosing the length, and tend to pick numbers fairly arbitrarily. We give a principled mathematical argument showing that it suffices for the length to be proportional to the number of desired number of edges. We also prescribe a method for choosing this proportionality constant. We run a series of experiments showing that the distributions of common graph properties converge in this time, providing empirical evidence for our claims.