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 Erdös-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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PACS: 02.50.-r; 89.75.Hc; 89.75.Da; 02.10.Ox
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Britton, T., Deijfen, M. & Martin-Löf, A. Generating Simple Random Graphs with Prescribed Degree Distribution. J Stat Phys 124, 1377–1397 (2006). https://doi.org/10.1007/s10955-006-9168-x
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DOI: https://doi.org/10.1007/s10955-006-9168-x