Constrained graph generation: Preserving diameter and clustering coefficient simultaneously

2026-02-23

AI Summary

This work addresses the challenge of generating graphs that simultaneously satisfy stringent structural constraints—such as prescribed diameter and clustering coefficient—a task where conventional methods struggle to effectively explore the feasible solution space. The authors propose a novel two-stage hybrid framework: first, a hierarchical ant colony optimization (ACO) performs globally guided search to efficiently produce constraint-compliant initial graphs; these graphs then serve as diverse seeds to drive Markov Chain Monte Carlo (MCMC) rewiring sampling, enhancing structural diversity. By integrating ACO with MCMC for the first time, the approach overcomes the sampling limitations of traditional MCMC caused by broken ergodicity, enabling efficient and diverse graph generation across disconnected regions of the solution space. Experiments demonstrate that, under various edge densities and constraint settings, the generated graphs not only meet structural requirements but also exhibit significantly improved diversity compared to standard MCMC.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

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
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Generating graphs subject to strict structural constraints is a fundamental computational challenge in network science. Simultaneously preserving interacting properties-such as the diameter and the clustering coefficient- is particularly demanding. Simple constructive algorithms often fail to locate vanishingly small sets of feasible graphs, while traditional Markov-chain Monte Carlo (MCMC) samplers suffer from severe ergodicity breaking. In this paper, we propose a two-step hybrid framework combining Ant Colony Optimization (ACO) and MCMC sampling. First, we design a layered ACO heuristic to perform a guided global search, effectively locating valid graphs with prescribed diameter and clustering coefficient. Second, we use these ACO-designed graphs as structurally distinct seed states for an MCMC rewiring algorithm. We evaluate this framework across a wide range of graph edge densities and varying diameter-clustering-coefficient constraint regimes. Using the spectral distance of the normalized Laplacian to quantify structural diversity of the resulting graphs, our experiments reveal a sharp contrast between the methods. Standard MCMC samplers remain rigidly trapped in an isolated subset of feasible graphs around their initial seeds. Conversely, our hybrid ACO-MCMC approach successfully bridges disconnected configuration landscapes, generating a vastly richer and structurally diverse set of valid graphs.

Problem

• constrained graph generation
• diameter
• clustering coefficient
• structural constraints
• network science

Innovation

• constrained graph generation
• ant colony optimization
• Markov chain Monte Carlo
• clustering coefficient
• graph diameter