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Markov chains are a convenient means of generating realizations of networks,since they require little more than a procedure for rewiring edges. If arewiring procedure exists for generating new graphs with specified statisticalproperties, then a Markov chain sampler can generate an ensemble of graphs withprescribed characteristics. However, successive graphs in a Markov chain cannotbe used when one desires independent draws from the distribution of graphs; therealizations are correlated. Consequently, one runs a Markov chain for Niterations before accepting the realization as an independent sample. In thiswork, we devise two methods for calculating N. They are both based on thebinary "time-series" denoting the occurrence/non-occurrence of edge (u, v)between vertices u and v in the Markov chain of graphs generated by thesampler. They differ in their underlying assumptions. We test them on thegeneration of graphs with a prescribed joint degree distribution. We find the Nproportional |E|, where |E| is the number of edges in the graph. The twomethods are compared by sampling on real, sparse graphs with 10^3 - 10^4vertices.

Are we there yet? When to stop a Markov chain while generating random graphs