受限图生成：同时保持直径和聚类系数
Constrained graph generation: Preserving diameter and clustering coefficient simultaneously
AI总结：
本文提出一种结合蚁群优化与MCMC的混合框架，用于生成同时保持直径和聚类系数的受限图，克服传统方法在结构多样性上的不足。
摘要：
在网络科学中，生成受严格结构约束的图是一个基本的计算挑战。同时保持交互性质——如直径和聚类系数——尤其具有挑战性。简单的构造算法往往无法定位极小的可行图集合，而传统的马尔可夫链蒙特卡洛（MCMC）采样器则面临严重的 ergodicity breaking 问题。在本文中，我们提出了一种两步混合框架，结合蚁群优化（ACO）和 MCMC 采样。首先，我们设计了一种分层 ACO 候选策略，进行引导的全局搜索，有效地定位具有指定直径和聚类系数的有效图。其次，我们使用这些 ACO 设计的图作为结构上不同的种子状态，用于 MCMC 重排算法。我们评估了该框架在广泛的图边密度和变化的直径-聚类系数约束范围内的表现。使用归一化拉普拉斯矩阵的谱距离来量化所生成图的结构多样性，我们的实验揭示了方法之间的鲜明对比。标准 MCMC 采样器仍被困在初始种子周围的孤立子集。相反，我们的混合 ACO-MCMC 方法成功地连接了不连通的配置景观，生成了大量丰富且结构多样的有效图。
英文摘要：
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.
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