Constrained graph generation: Preserving diameter and clustering coefficient simultaneously
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arXiv
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| Format: | Preprint |
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2026
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| author | Ferenczi, Dávid Grigoriev, Alexander |
| author_facet | Ferenczi, Dávid Grigoriev, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19595 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constrained graph generation: Preserving diameter and clustering coefficient simultaneously Ferenczi, Dávid Grigoriev, Alexander Social and Information Networks Discrete Mathematics Probability 05C80, 65C05 G.2.2; G.3 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. |
| title | Constrained graph generation: Preserving diameter and clustering coefficient simultaneously |
| topic | Social and Information Networks Discrete Mathematics Probability 05C80, 65C05 G.2.2; G.3 |
| url | https://arxiv.org/abs/2602.19595 |