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.
[1]
Matthias Müller-Hannemann,et al.
Uniform sampling of undirected and directed graphs with a fixed degree sequence
,
2009,
ArXiv.
[2]
A. Rao,et al.
A Markov chain Monte carol method for generating random (0, 1)-matrices with given marginals
,
1996
.
[3]
Michael Drew Lamar.
Algorithms for realizing degree sequences of directed graphs
,
2009,
ArXiv.
[4]
Yung-Pin Chen,et al.
An Application of Markov Chain Monte Carlo to Community Ecology
,
2003,
Am. Math. Mon..
[5]
Sulamita Klein,et al.
List Partitions
,
2003,
SIAM J. Discret. Math..
[6]
John M. Roberts.
Simple methods for simulating sociomatrices with given marginal totals
,
2000,
Soc. Networks.