Graph Generation Methods under Partial Information

2026-03-11

AI Summary

This work addresses the classical challenge of efficiently generating bipartite, directed, and undirected graphs that satisfy prescribed degree sequences when only local node-degree information is available. The authors propose a sequential graph construction method that, for the first time, rigorously characterizes the necessary and sufficient feasibility interval for the number of connections at each step, thereby guaranteeing global realizability while unifying the treatment of all three graph types. Building on this theoretical foundation, they develop a versatile algorithm capable of both exhaustive enumeration and uniform random sampling, supporting symmetric connections and scaling to large-scale instances. Experimental results demonstrate that the proposed approach substantially outperforms existing methods in computational efficiency and scalability, effectively overcoming the performance bottleneck in large-scale graph generation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Security and Privacy: Large-scale security measurements

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.

Problem

• graph generation
• degree sequence
• bipartite graph
• directed graph
• undirected graph

Innovation

• graph generation
• degree sequence
• sequential algorithm
• feasibility condition
• scalable sampling