Graph Generation Methods under Partial Information

TL;DR

This paper introduces new algorithms for generating graphs with specific degree sequences across bipartite, directed, and undirected networks, ensuring feasibility and scalability for large instances.

Contribution

It presents a sequential bipartite graph generation method with a necessary and sufficient feasibility condition, extending it to directed and undirected graphs with efficient algorithms.

Findings

Algorithms successfully generate large graphs with prescribed degrees.

Methods outperform existing approaches in scalability.

Numerical experiments confirm the algorithms' efficiency.

Abstract

We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient interval condition that characterizes the admissible number of connections at each step, thereby guaranteeing global feasibility. Based on this result, we develop bipartite graph enumeration and sampling algorithms suitable for different problem sizes. We then extend these bipartite graph algorithms to the directed and undirected cases by incorporating additional connection constraints, as well as feasibility verification and symmetric connection steps, while preserving the same algorithmic principles. Finally, numerical experiments demonstrate the performance of the proposed algorithms, particularly their scalability to large instances where existing methods become computationally prohibitive.