Sufficient Conditions for Graphicality of Bidegree Sequences

TL;DR

This paper introduces new, easy-to-apply sufficient conditions for determining if a bidegree sequence can be realized by a directed graph, expanding the toolkit for graph generation and analysis.

Contribution

The authors propose novel sufficient graphicality criteria based on sequence length and mean degree, which are simpler and more flexible than existing conditions.

Findings

Conditions are easier to verify than classic inequalities.

Criteria cover some sequences not addressed by previous conditions.

Results facilitate graph generation with specified degree sequences.

Abstract

There are a variety of existing conditions for a degree sequence to be graphic. When a degree sequence satisfies any of these conditions, there exists a graph that realizes the sequence. We formulate several novel sufficient graphicality criteria that depend on the number of elements in the sequence, corresponding to the number of nodes in an associated graph, and the mean degree of the sequence. These conditions, which are stated in terms of bidegree sequences for directed graphs, are easier to apply than classic necessary and sufficient graphicality conditions involving multiple inequalities. They are also more flexible than more recent graphicality conditions, in that they imply graphicality of some degree sequences not covered by those conditions. The form of our results will allow them to be easily used for the generation of graphs with particular degree sequences for applications.