This paper presents the application of a graph-based methodology for the assessment of flood impacts in an urban context. In this methodology, exposed elements are organized as nodes on a graph, which is used to propagate impacts from directly affected nodes to other nodes across graph links. Compared to traditional approaches, the main advantage of the adopted methodology lies in the possibility of identifying and understanding indirect impacts and cascading effects. The application case concerns floods numerically reconstructed in Mexico City in response to rainfall events of increasing return periods. The hazard reconstruction was carried out by using a simplified hydrological/hydraulic model of the urban drainage system, implemented in EPASWMM, the Storm Water Management Model developed by the United States Environmental Protection Agency. The paper shows how the impacts are propagated along different orders of the impact chain for each return period and compares the risk curves between direct and indirect impact. It also highlights the extent to which the reduction in demand of services from consumers and the loss of services from suppliers are respectively contributing to the final indirect impacts. Finally, it illustrates how different impact mitigation measures can be formulated based on systemic information provided by the analysis of graph properties and taking into account indirect impacts.

Abstract. Assessing the risk of complex systems to natural hazards is an important but challenging problem. In today's intricate socio-technological world, characterized by strong urbanization and technological trends, the connections and interdependencies between exposed elements are crucial. These complex relationships call for a paradigm shift in collective risk assessments, from a reductionist approach to a holistic one. Most commonly, the risk of a system is estimated through a reductionist approach, based on the sum of the risk evaluated individually at each of its elements. In contrast, a holistic approach considers the whole system to be a unique entity of interconnected elements, where those connections are taken into account in order to assess risk more thoroughly. To support this paradigm shift, this paper proposes a holistic approach to analyse risk in complex systems based on the construction and study of a graph, the mathematical structure to model connections between elements. We demonstrate that representing a complex system such as an urban settlement by means of a graph, and using the techniques made available by the branch of mathematics called graph theory, will have at least two advantages. First, it is possible to establish analogies between certain graph metrics (e.g. authority, degree and hub values) and the risk variables (exposure, vulnerability and resilience) and leverage these analogies to obtain a deeper knowledge of the exposed system to a hazard (structure, weaknesses, etc.). Second, it is possible to use the graph as a tool to propagate the damage into the system, for not only direct but also indirect and cascading effects, and, ultimately, to better understand the risk mechanisms of natural hazards in complex systems. The feasibility of the proposed approach is illustrated by an application to a pilot study in Mexico City.

Abstract. Assessing the risk of complex systems to natural hazards is an important and challenging problem. In today’s intricate socio-technological world, characterized by strong urbanization and technological trends, the connections, interdependencies and interactions between exposed elements are crucial. These complex relations call for a paradigm shift in collective risk assessments, from a reductionist approach to a holistic one. Most commonly, the risk of a system is estimated through a reductionist approach, based on the sum of the risk of its elements individually. In contrast, a holistic approach considers the whole system as a unique entity of interconnected elements, where those connections are taken into account in order to more thoroughly assess risk. To support this paradigm shift, this paper proposes a new holistic approach to assess the risk in complex systems based on Graph Theory. The paper is organized in two parts: part I describes the proposed approach, and part II presents an application to a pilot study in Mexico City. In part I, we demonstrate that by representing a complex system such as an urban settlement by means of a network (i.e. a graph), it is possible to take advantage of the techniques made available by the branch of mathematics called Graph Theory to analyse its properties. Moreover, it is possible to establish analogies between certain graph metrics (e.g. authority, degree, hub values) and risk variables (exposure, vulnerability and resilience). Leveraging these analogies, one can not only obtain a deeper knowledge of the system (structure, weaknesses, etc.), but also understand its risk mechanisms (how the impacts of a single or multiple natural hazards are propagated, where they are exacerbated), and therefore assess the disaster risk of the system as a whole, including second-order impacts and cascade effects.

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The development of strategies to adapt to and mitigate the potential adverse consequences of natural hazards requires support from risk assessment studies that quantify the impacts of hazardous events on our society. A comprehensive analysis of risk commonly evaluates the elements exposed to the hazard probabilistic scenarios and their vulnerabilities. However, while significant advances have been made in the assessment of direct losses, indirect impacts are less frequently examined. This work assesses the indirect consequences of two hydrologic hazards, i.e., pluvial and fluvial floods, in an urban context from a system perspective. It presents a methodology to estimate the services accessibility risk (SAR) that considers the accessibility of roads and the connection between providers and users of services in a city. The feasibility of the proposed approach is illustrated by an application to a pilot study in Monza city (northern Italy) considering pluvial and fluvial flood hazard with different return periods. The results in terms of the social and economic impacts are analyzed considering features of age, disability, and the different economic sectors.