The Shape of Water Distribution Systems - Describing local structures of water networks via graphlet analysis

Abstract

The performance, vulnerability, and resilience of water distribution systems (WDS) are connected to its underlying topological structure (aka its shape). The literature mostly differentiates between two main shapes of networks - branched or looped. However, real networks come in various shapes and forms spanning between the two extremes of purely branched and looped types. Although these networks are globally topologically different, they may show high similarity on the local scale of a borough or a neighbourhood, or vice versa. Recent studies focused on describing WDS via graph theory representing pipes as edges and customers, tanks, and reservoirs as nodes, for example. The first attempt of graph theoretical applications showed promising results in estimating the global resilience of WDS, but there is a limited number of metrics that take the importance of local topology into consideration. Furthermore, iterative estimation of local vulnerability by simulating faults in each element of the system is prohibitively expensive from a computational point of view (i.e., various hydraulic simulations for assessing the vulnerability of each part of the system are needed).This research enters the new terrain of local WDS investigations through graphlet analysis. Graphlets are small connected subgraphs of a large network and have recently gathered much attention as a useful concept to describe local topology and uncover structural design principles of complex networks. Consequently, these novel analyses techniques can provide deep insights into how local WDS structures influence their overall performance.In this work, we investigate the influence of local network structures on the resilience of entire networks through graphlet analysis. First, we calculate local vulnerability of the network elements and global resilience indicators (i.e. Todini index, pipe and node criticality indices). We additionally simulate fault scenarios with EPANET and evaluate volumes of unsupplied demand on a multitude of real WDS. Second, we investigate the graphlet substructure of those WDSs to assess how much of the network’s vulnerability can be described by purely looking at the topology. First results show that graphlet representation of local neighbourhoods can serve as an efficient proxy metric capable of replacing computationally heavy performance analysis based on extensive hydraulic simulation. We additionally compare the influence of local changes on subgraphs to show how local changes in network design may grant improved robustness against such failures, ultimately increasing global resilience based on changing local topology. Urban water management can benefit from the proposed approach by not only identifying the most vulnerable elements of the critical infrastructure but providing insight into how to build globally more resilient WDS networks by enforcing small and therefore economical topological changes.