网络拆解中的临界性与普适性
Criticality and universality in network dismantling
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中文总结 AI 辅助
该研究针对网络拆解问题，引入自适应偏向渗流过程，发现其存在普适相变，且网络拆解的物理特性对拓扑性质不敏感，有望开发拓扑无关的临界行为解释理论。
中文摘要 AI 辅助
识别移除后能拆解复杂网络的最小元素集合，即网络拆解问题，是一项具有诸多实际应用的基础任务。过去十年间，网络拆解已得到广泛研究，但多数工作聚焦于为大型有限网络开发高效算法。相比之下，网络拆解过程的物理学，即移除节点或边如何影响网络结构连通性，在热力学极限下仍基本未被探索。本文通过引入一种自适应偏向渗流过程，该过程可最优地拆解网络，阐明了网络拆解这一未被充分研究的方面。通过对合成网络模型的系统分析，我们发现所提出的渗流过程呈现出普适相变，其特征是巨型连通分量与最大2-核同时突然消失，且这一相变在度分布显著不同的网络中均存在。对真实网络的模拟进一步支持了这一普适性，表明网络拆解的物理学对广泛的拓扑性质不敏感。综合来看，这些结果表明可以开发一种与拓扑无关的理论来解释网络拆解的临界行为。
英文摘要
Identifying the smallest set of elements whose removal dismantle a complex network, known as the network dismantling problem, is a fundamental task with many practical applications. Whereas network dismantling has been extensively studied over the past decade, most work has focused on developing efficient algorithms for large but finite networks. By contrast, the physics of the network dismantling process, namely how the network structural connectivity is affected by the removal of nodes or edges, remains largely unexplored in the thermodynamic limit. Here, we shed light on this understudied aspect of network dismantling by introducing an adaptive biased percolation process able to optimally dismantle a network. Through a systematic analysis of synthetic network models, we find that the proposed percolation process displays a universal phase transition, characterized by the abrupt and simultaneous disappearance of both the giant connected component and the largest 2-core, across networks with markedly different degree distributions. Simulations on real networks further support this universality, indicating that the physics of network dismantling is insensitive to a broad range of topological properties. Together, these results suggest that a topology-agnostic theory could be developed to explain the critical behavior of network dismantling.
