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.

翻译：在约束条件下生成满足严格结构要求的图是网络科学中的一个基本计算挑战。同时保持相互作用的属性——如直径与聚类系数——尤为困难。简单的构造算法通常无法定位到极其微小的可行图集合，而传统的马尔可夫链蒙特卡洛（MCMC）采样器则遭受严重的遍历性破坏。本文提出一种结合蚁群优化（ACO）与MCMC采样的两步混合框架。首先，我们设计了一种分层ACO启发式算法以执行引导式全局搜索，有效定位具有指定直径与聚类系数的有效图。其次，我们将这些ACO设计的图作为结构上不同的种子状态，用于MCMC重连算法。我们在广泛的图边密度以及不同的直径-聚类系数约束机制下评估该框架。通过使用归一化拉普拉斯矩阵的谱距离来量化所得图的结构多样性，实验结果显示方法之间存在鲜明对比。标准MCMC采样器严格地被困在其初始种子周围的孤立可行图子集中。相反，我们的混合ACO-MCMC方法成功桥接了不连通的配置空间，生成了远为丰富且结构多样的有效图集合。