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Choosing a uniformly sampled simple directed graph realization of a degreesequence has many applications, in particular in social networks whereself-loops are commonly not allowed. It has been shown in the past that one canperform a Markov chain arc-switching algorithm to sample a simple directedgraph uniformly by performing two types of switches: a 2-switch and a directed3-cycle reorientation. This paper discusses under what circumstances a directed3-cycle reorientation is required. In particular, the class of degree sequenceswhere this is required is a subclass of the directed 3-cycle anchored degreesequences. An important implication of this result is a reduced Markov chainalgorithm that uses only 2-switches.

On uniform sampling simple directed graph realizations of degree sequences