Interdependencies between city water and electricity supply networks based on attack tolerance

Historical events suggest that infrastructure interdependencies exhibit negative influence in an amplifying or cascading way, leading to remarkably outcomes on an urban, regional, or even national scale. Therefore, studies on infrastructure interdependencies play a vital role. The interdependency-caused vulnerability of water and electricity supply networks, as components of city lifeline, generally poses risks to people's life safety, daily life, and industry functioning.

A case study of water and electricity supply networks of a district was conducted to measure their interdependencies in the frame of attack tolerance, thus innovatively advancing from its usual use in studies on the World Wide Web and social networks. Infrastructure systems tend to possess certain spatial structures, especially network-like ones such as water and electricity supply networks, rendering topological methods effective and straightforward. An attack tolerance framework based on graph theory was applied in this research. Two graph models were established using the Python NetworkX library prior to checking the correctness of the modeling. The degree of each vertex was calculated, and its frequency density curve was drawn to match the network characteristics with those of an exponential network, such as a water or electricity supply network. Subsequently, the fragmentation of the networks was studied. When the vertices were removed to simulate a random external attack, the original network as a whole disintegrated into multiple disconnected small components known as vertex clusters. This process is called fragmentation. The quantitative characteristics of vertex clusters, together with the basic network index called network diameter, served as indices of attack tolerance. The curves of the indices above the proportion of removed vertices and the distribution scatters of cluster size at a certain removed proportion were drawn to measure and compare the attack tolerance between the two networks. In addition, the distribution scatters were fit to an exponential form including two parameters and the curve of the parameters to the removed proportion was drawn. Finally, this study introduced a measure of geographical interdependency between water and electricity networks based on a previous attack tolerance study. The two networks were placed in the same coordination system that had been gridded rectangularly with a certain fineness. The hypothesis was that the electricity of each water vertex was provided by the nearest electricity vertex; the former was removed when the latter malfunctions. Vertices in each rectangle of the grid were completely removed to simulate a blackout of a district, and a geographical interdependency index was defined for every grid reference in accordance with the fragmentation indices. This research visualized the spatial distribution of the interdependency index at a certain grid fineness, through which the critical sections could be identified.

The attack tolerance of the water supply network was slightly remarkable, and the southeast region of the water supply network of this district was the most dependent on the electricity supply network.

This work introduced an interdependency analysis method based on the framework of attack tolerance of a topological network and provided guidelines for the protection of infrastructure systems, urban planning, contingency plans, and resilience enhancements.