Centre for Advanced Spatial Analysis (CASA), UCL, 90 Tottenham Court Rd., London, W1T 4TJ, UK.
Consumer Data Research Centre (CDRC), UCL, Pearson Building, Gower Street, London, WC1E 6BT, UK.
Sci Rep. 2017 Jun 27;7(1):4312. doi: 10.1038/s41598-017-04477-z.
Road networks are characterised by several structural and geometrical properties. The topological structure determines partially the hierarchical arrangement of roads, but since these are networks that are spatially constrained, geometrical properties play a fundamental role in determining the network's behaviour, characterising the influence of each of the street segments on the system. In this work, we apply percolation theory to the UK's road network using the relative angle between street segments as the occupation probability. The appearance of the spanning cluster is marked by a phase transition, indicating that the system behaves in a critical way. Computing Shannon's entropy of the cluster sizes, different stages of the percolation process can be discerned, and these indicate that roads integrate to the giant cluster in a hierarchical manner. This is used to construct a hierarchical index that serves to classify roads in terms of their importance. The obtained classification is in very good correspondence with the official designations of roads. This methodology hence provides a framework to consistently extract the main skeleton of an urban system and to further classify each road in terms of its hierarchical importance within the system.
道路网络具有多种结构和几何属性。拓扑结构部分决定了道路的层次排列，但由于这些是空间受限的网络，因此几何属性在确定网络行为方面起着至关重要的作用，从而描述了每个街道段对系统的影响。在这项工作中，我们使用街道段之间的相对角度作为占据概率，将渗流理论应用于英国的道路网络。跨越簇的出现标志着相变的发生，表明系统以临界方式表现。通过计算簇大小的香农熵，可以分辨出渗流过程的不同阶段，这表明道路以分层的方式整合到巨大的簇中。这用于构建一个层次索引，用于根据其重要性对道路进行分类。所得到的分类与道路的官方指定非常吻合。因此，该方法为一致地提取城市系统的主要骨架提供了一个框架，并进一步根据道路在系统中的层次重要性对其进行分类。
