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arXiv · 1509.06985

Generating simple random graphs with prescribed degree distribution

Tom Britton·Maria Deijfen·Anders Martin-Löf
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Abstract

Let $F$ be a probability distribution with support on the non-negative integers. Four methods for generating a simple undirected graph with (approximate) degree distribution $F$ are described and compared. Two methods are based on the so called configuration model with modifications ensuring a simple graph, one method is an extension of the classical Erdős-Rényi graph where the edge probabilities are random variables, and the last method starts with a directed random graph which is then modified to a simple undirected graph. All methods are shown to give the correct distribution in the limit of large graph size, but under different assumptions on the degree distribution $F$ and also using different order of operations.

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Tom Britton, Maria Deijfen, Anders Martin-Löf. 2015-09-23. Generating simple random graphs with prescribed degree distribution. https://doi.org/10.1007/s10955-006-9168-x

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