Abstract
The issue of vulnerability and robustness in networks have been addressed by several methods. The goal is to identify which are the critical components (i.e., nodes/edges) whose failure impairs the functioning of the network and how much this impacts the ensuing increase in vulnerability. In this paper we consider the drop in the network robustness as measured by the increase in vulnerability of the perturbed network and compare it with the original one. Traditional robustness metrics are based on centrality measures, the loss of efficiency and spectral analysis. The approach proposed in this paper sees the graph as a set of probability distributions and computes, specifically the probability distribution of its node to node distances and computes an index of vulnerability through the distance between the node-to-node distributions associated to original network and the one obtained by the removal of nodes and edges. Two such distances are proposed for this analysis: Jensen–Shannon and Wasserstein, based respectively on information theory and optimal transport theory, which are shown to offer a different characterization of vulnerability. Extensive computational results, including two real-world water distribution networks, are reported comparing the new approach to the traditional metrics. This modelling and algorithmic framework can also support the analysis of other networked infrastructures among which power grids, gas distribution and transit networks.
Highlights
Overview and motivationRobustness and resilience describe the capability of the network to withstand failures and perturbations in its components and keep delivering services regardless of disruptive events, either random or malicious, as, in a water distribution network (WDN), failures in pumping stations or valves and severe bursts in the main pipes.Resilience, robustness, reliability and vulnerability are terms strictly linked and often confusingly used
Experimental setting and computational results In our problem the network space is given by the basic network G and the subgraphs obtained by the removal of one or more edges
The main result of this paper is that probabilistic measures based on the probability distribution of node–node distances, yield a distance, between the original network and that resulting from the removal of some nodes/edges, which can provide a set of indicators of the increase in vulnerability
Summary
Robustness and resilience describe the capability of the network to withstand failures and perturbations in its components and keep delivering services regardless of disruptive events, either random or malicious, as, in a water distribution network (WDN), failures in pumping stations or valves and severe bursts in the main pipes. The main contribution of this paper is the introduction of a new set of vulnerability metrics given by the distance between the probability distributions of node–node distances between the original network and that resulting from the removal of nodes/ edges. These metrics allow the formulation of measures of criticality of single edges in the network. Experimental setting and computational results In our problem the network space is given by the basic network G and the subgraphs obtained by the removal of one or more edges The elements of this space are represented as probability distributions of node-2-node distances (Eq 1) and aggregated into a distributional representations of the basic network and of the subgraphs (Eq 2).
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