water Article Assessment of the Disaster Resilience of Complex Systems: The Case of the Flood Resilience of a Densely Populated City Marcello Arosio * , Luigi Cesarini and Mario L. V. Martina   Citation: Arosio, M.; Cesarini, L.; Martina, M.L.V. Assessment of the Disaster Resilience of Complex Systems: The Case of the Flood Resilience of a Densely Populated City. Water 2021, 13, 2830. https:// doi.org/10.3390/w13202830 Academic Editor: Yurui Fan Received: 30 August 2021 Accepted: 7 October 2021 Published: 12 October 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Department of Sciences, Technologies and Society, Scuola Universitaria Superiore IUSS Pavia, 27100 Pavia, Italy; luigi.cesarini@iusspavia.it (L.C.); mario.martina@iusspavia.it (M.L.V.M.) * Correspondence: marcello.arosio@iusspavia.it Abstract: In the last decades, resilience became officially the worldwide cornerstone to reduce the risk of disasters and improve preparedness, response, and recovery capacities. Although the concept of resilience is now clear, it is still under debate how to model and quantify it. The aim of this work was to quantify the resilience of a complex system, such as a densely populated and urbanized area, by modelling it with a graph, the mathematical representation of the system element and connections. We showed that the graph can account for the resilience characteristics included in its definition according to the United Nations General Assembly, considering two significant aspects of this definition in particular: (1) resilience is a property of a system and not of single entities and (2) resilience is a property of the system dynamic response. We proposed to represent the exposed elements of the system and their connections (i.e., the services they exchange) with a weighted and redundant graph. By mean of it, we assessed the systemic properties, such as authority and hub values and highlighted the centrality of some elements. Furthermore, we showed that after an external perturbation, such as a hazardous event, each element can dynamically adapt, and a new graph configuration is set up, taking advantage of the redundancy of the connections and the capacity of each element to supply lost services. Finally, we proposed a quantitative metric for resilience as the actual reduction of the impacts of events at different return periods when resilient properties of the system are activated. To illustrate step by step the proposed methodology and show its practical feasibility, we applied it to a pilot study: the city of Monza, a densely populated urban environment exposed to river and pluvial floods. Keywords: resilience; disaster; urban; pluvial flood; river flood; graph theory; systemic risk; complex system 1. Introduction At the Third World Conference on Disaster Risk Reduction (3rd WCDRR, Sendai, 2015), states confirmed their commitment to disaster risk reduction by building societies more resilient to disasters. With this stance, resilience became officially the foundation of the disasters risk reduction components: preparedness, response, and recovery capacities. The institutional recognition of the resilience role is part of a long process with broad and deep debate in the scientific community and beyond [1]. The origin and etymology of the concept of resilience derive from the Latin word resilio or resilire, which means “to jump back” [2,3] and its evolution until today and its relevance to the context of disaster risk reduction is well represented in Alexander (2013) [4]. According to C. G. Burton (2015) [5], Timmerman in 1981 [6] was the first author to coin the term resilience in the scientific context of natural hazards and disasters, and in his work, resilience represents the measure of “the capacity of a system, or part of a system, to absorb or recover from an adverse event”. At the beginning of the 21st century, Adger (2000) [7] extended Holling’s concept of ecological resilience to human communities. During the last thirty years, reaching an agreement on what resilience means has been one of the most intense debates in the academic and institutional spheres [8]. In parallel Water 2021, 13, 2830. https://doi.org/10.3390/w13202830 https://www.mdpi.com/journal/water