负荷作用下城市电网的解体模式
On the breakup patterns of urban networks under load
摘要：
伦敦和纽约市的城市网络进行了研究，作为有向图的图形渗透的范式。最近观察到，当一小部分边缘被移除时，城市网络表现出临界渗流转变。由此产生的强连接组件形成一个集群结构，其尺寸分布遵循幂律与临界指数$τ$。我们首先分析了网络在受到越来越广泛的随机边缘去除以及具有幂律衰减的空间相关性的影响时的反应。我们观察到随着空间相关性的增加，$τ$逐渐减少。当使用真实交通数据（UBER）来删除拥塞图边缘时，会发生类似的现象：在低拥塞期间，$τ$接近于针对不相关渗流获得的指数，而在高峰时段，指数变得更接近于从空间相关边缘去除获得的指数。我们发现，空间相关性似乎发挥了重要的作用，不同的交通模式。我们最后提出了一些初步证据，表明在临界状态下，最大的集群显示出空间可预测性，并且集群配置形成了一个具有很少主要分支的分类法：只存在有限数量的分解模式，具体针对每个城市。这适用于随机渗流和真实交通，其中三个最大的集群是本地化和空间上不同的。这种一致的集群组织受到当地地形结构（如河流和桥梁）的强烈影响。
英文摘要：
The urban networks of London and New York City are investigated as directed graphs within the paradigm of graph percolation. It has been recently observed that urban networks show a critical percolation transition when a fraction of edges are removed. The resulting strongly connected components form a cluster structure whose size distribution follows a power law with critical exponent $τ$. We start by analyzing how the networks react when subjected to increasingly widespread random edge removal and the effect of spatial correlations with power-law decay. We observe a progressive decrease of $τ$ as spatial correlations grow. A similar phenomenon happens when real traffic data (UBER) is used to delete congested graph edges: during low congestion periods $τ$ is close to that obtained for uncorrelated percolation, while during rush hours the exponent becomes closer to the one obtained from spatially correlated edge removal. We show that spatial correlations seem to play an important role to model different traffic regimes. We finally present some preliminary evidence that, at criticality, the largest clusters display spatial predictability and that cluster configurations form a taxonomy with few main clades: only a finite number of breakup patterns, specific for each city, exists. This holds both for random percolation and real traffic, where the three largest clusters are well localized and spatially distinct. This consistent cluster organization is strongly influenced by local topographical structures such as rivers and bridges.
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