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.