Entropy of centrality values for topological vulnerability analysis of water distribution networks

Purpose The increased complexity of water distribution networks (WDNs) emphasizes the importance of studying the relationship between topology and vulnerability of these networks. However, the few existing studies on this subject measure the vulnerability at a specific location and ignore to quantify the vulnerability as a whole. The purpose of this paper is to fill this gap by extending the topological vulnerability analysis further to the global level. Design/methodology/approach This paper introduces a two-step procedure. In the first step, this work evaluates the degree of influence of a node by employing graph theory quantities. In the second step, information entropy is used as a tool to quantify the global vulnerability of WDNs. Findings The vulnerability analysis results showed that a network with uniformly distributed centrality values exhibits a lower drop in performance in the case of partial failure of its components and therefore is less vulnerable. In other words, the failure of a highly central node leads to a significant loss of performance in the network. Practical implications The vulnerability analysis method, developed in this work, provides a decision support tool to implement a cost-effective maintenance strategy, which relies on identifying and prioritizing the vulnerabilities, thereby reducing expenditures on maintenance activities. Originality/value By situating the research in the entropy theory context, for the first time, this paper demonstrates how heterogeneity and homogeneity of centrality values measured by the information entropy can be interpreted in terms of the network vulnerability.

Vulnerability analysis in Complex Networks under a Flood Risk Reduction point of view

The measurement and mapping of transportation network vulnerability constitute subjects of global interest. During a flood, some elements of a transportation network can be reached, causing damages directly (to people, vehicles and roads/streets) and indirect damages (services) with great economic impacts. The Complex Networks approach may offer a valuable perspective considering one type of vulnerability especially related to Disaster Risk Reduction on critical infrastructures: the topological vulnerability. The topological vulnerability index associated to an element in a graph is defined as the damage (variation) on the network’s average efficiency due to the removal of that element. We have performed a topological vulnerability analysis to the highways in the state of Santa Catarina (Brazil), and produced a risk map considering that index and the flood susceptible areas. Our results can represent an important tool for stakeholders from the transportation sector.