On uniform sampling simple directed graph realizations of degree sequences

Details On uniform sampling simple directed graph realizations of degree sequences On uniform sampling simple directed graph realizations of degree sequences

2009-12-21

arxiv.org/abs/0912.3834v1

Computer Science

Discrete Mathematics

7 pages, 4 figures

Scientific paper

Choosing a uniformly sampled simple directed graph realization of a degree sequence has many applications, in particular in social networks where self-loops are commonly not allowed. It has been shown in the past that one can perform a Markov chain arc-switching algorithm to sample a simple directed graph uniformly by performing two types of switches: a 2-switch and a directed 3-cycle reorientation. This paper discusses under what circumstances a directed 3-cycle reorientation is required. In particular, the class of degree sequences where this is required is a subclass of the directed 3-cycle anchored degree sequences. An important implication of this result is a reduced Markov chain algorithm that uses only 2-switches.

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