## A sequential importance sampling algorithm for generating random graphs with prescribed degrees (2006)

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### BibTeX

@TECHREPORT{Blitzstein06asequential,

author = {Joseph Blitzstein and Persi Diaconis},

title = {A sequential importance sampling algorithm for generating random graphs with prescribed degrees},

institution = {},

year = {2006}

}

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### Abstract

Random graphs with a given degree sequence are a useful model capturing several features absent in the classical Erdős-Rényi model, such as dependent edges and non-binomial degrees. In this paper, we use a characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows surprisingly efficient sequential importance sampling. Applications are given, including simulating a biological network and estimating the number of graphs with a given degree sequence. 1. Introduction. Random