Topological data analysis for resilience assessment of water distribution networks

Water Distribution Networks (WDNs) are critical assets, that are required to provide safe drinking water under a wide range of operational and management conditions, including failures. Understanding the structural properties of a water distribution system in different disruptive event scenarios is a key aspect of improving the security, reliability, and efficiency of the WDNs. In particular, the identification of critical components whose failure can negatively influence network performances and system resilience has direct relevance for decision-makers involved in planning, management, and improvement activities. The study of WDNs, structured as mathematical objects, can be carried on with different mathematical approaches. Among the many methods and tools available, the use of topological indicators and, in particular, Topological Data Analysis (TDA) has emerged as a cutting-edge tool in this field. In this work, we propose persistent homology to derive a new metric for the resilience of water networks, which, together with the other metrics known in the literature, can provide a more complete description of the system.