Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 124, Issue 6, Pages 1377-1397Publisher
SPRINGER
DOI: 10.1007/s10955-006-9168-x
Keywords
simple graphs; random graphs; degree distribution; generating algorithms; configuration model
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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 Erdos-Renyi 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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