Vulnerability analysis of transportation networks has rapidly become important in recent decades given the increasing numbers of transportation disasters. In this paper, we describe a method for calculating the minimum cuts between all pairs of nodes in a transportation network and develop two indices for analyzing vulnerability; these are derived from topology-based vulnerability/demand-accountable analyses and enable evaluation of cuts without assuming route-choice behaviors. We show that such analyses can be performed using a Gomory–Hu tree to reduce the computational load. This method is efficient, requiring only N − 1 calculations of the maximum flow problem even though the number of node pairs is N², where N is the number of nodes. In addition, we show that the total demand passing each minimum cut, which is necessary for demand-accountable analysis, can be obtained by network loading onto the tree using the Gomory–Hu tree features. We apply the proposed method to the central region of Japan to illustrate the applicability of the two indices for identifying vulnerable links in the road network.

近几十年来，随着交通灾害数量的增加，交通网络的脆弱性分析变得越来越重要。在本文中，我们描述了一种计算交通网络中所有节点对之间的最小割量的方法，并开发了两个用于分析脆弱性的指标；这些来自基于拓扑的脆弱性/需求责任分析，并且可以在不假设路线选择行为的情况下评估削减。我们表明可以使用 Gomory-Hu 树执行此类分析以减少计算负载。这种方法是有效的， 即使节点对数为N ²，也只需要对最大流问题进行N − 1 次计算，其中N是节点数。此外，我们表明，通过使用 Gomory-Hu 树特征的网络加载到树上，可以获得通过每个最小割的总需求，这是需求负责分析所必需的。我们将所提出的方法应用于日本中部地区，以说明这两个指数在识别道路网络中的脆弱链接方面的适用性。