## Our Methodology

**Identify relevant typologies of exposed elements**

The nodes of the graph can theoretically represent all the entities that the analysis wants to consider: physical elements like a single building, bridge and electric tower, suppliers of services such as schools, hospitals and fire brigades, or beneficiaries such as population, students or specific vulnerable groups such as elderly people. Due to the very wide variety of elements that can be chosen, it is necessary to select the most relevant category of nodes to the specific context of analysis.

**Define connection between typologies**

The links between the nodes that create the graph can range from physical, geographical, cyber or logical connections. Depending on the selected category for the node, it is necessary to define the type of connection between elements, which are essential for the analysis, and its characteristics: direction and weight.

**Define rules between elements**

The rules establish the connections between each single node. For the sake of clarity, an example could be the following: in the conceptual network, the relationship is defined between students and school (“students go to school”); subsequently, it is necessary to make the link between each student and a school in the area, applying the following rule – “students go to the closest school”.

**Built graph**

The list of nodes, together with either the list of links, are the inputs to build the mathematical graph using dedicated tools. For example, in NEWFRAME we use the igraph package (http://igraph.org/r/), the specific library and package for network analysis of the R environment. It provides a set of data types and functions for the implementation of graph algorithms, and it is able to handle large graphs with millions of vertices and edges.

**Analyse properties and cascading effects**

The relevant graph properties are computed and interpreted from a natural hazard risk perspective. Analysing the properties of the entire graph allows looking at the studied system as a unique entity that results from the connections and interactions between its parts. These global properties show how the whole system is vulnerable to an external perturbation, as for example a hazardous event that can affect part of it. In parallel, the approach allow to assess the properties of the single nodes of the graph in order to check which element, or set of elements, are more critical for the entire system.

## Assess and analyse risk

In order to assess risk and realize a proper DRR strategy, the information provided by the analysis of graph properties needs to be integrated and overlapped with hazard information (e.g. intensity, extension, probability of occurrence). Finally, it is necessary to integrate the hazard for different return periods with the exposed network to assess the total impact, direct and indirect.

**Identify relevant typologies of exposed elements**

The nodes of the graph can theoretically represent all the entities that the analysis wants to consider: physical elements like a single building, bridge and electric tower, suppliers of services such as schools, hospitals and fire brigades, or beneficiaries such as population, students or specific vulnerable groups such as elderly people. Due to the very wide variety of elements that can be chosen, it is necessary to select the most relevant category of nodes to the specific context of analysis.

**Define connection between typologies**

The links between the nodes that create the graph can range from physical, geographical, cyber or logical connections. Depending on the selected category for the node, it is necessary to define the type of connection between elements, which are essential for the analysis, and its characteristics: direction and weight.

**Define rules between elements**

The rules establish the connections between each single node. For the sake of clarity, an example could be the following: in the conceptual network, the relationship is defined between students and school (“students go to school”); subsequently, it is necessary to make the link between each student and a school in the area, applying the following rule – “students go to the closest school”.

**Built graph**

The list of nodes, together with either the list of links, are the inputs to build the mathematical graph using dedicated tools. For example, in NEWFRAME we use the igraph package (http://igraph.org/r/), the specific library and package for network analysis of the R environment. It provides a set of data types and functions for the implementation of graph algorithms, and it is able to handle large graphs with millions of vertices and edges.

**Analyse properties and cascading effects**

The relevant graph properties are computed and interpreted from a natural hazard risk perspective. Analysing the properties of the entire graph allows looking at the studied system as a unique entity that results from the connections and interactions between its parts. These global properties show how the whole system is vulnerable to an external perturbation, as for example a hazardous event that can affect part of it. In parallel, the approach allow to assess the properties of the single nodes of the graph in order to check which element, or set of elements, are more critical for the entire system.

## Assess and analyse risk

In order to assess risk and realize a proper DRR strategy, the information provided by the analysis of graph properties needs to be integrated and overlapped with hazard information (e.g. intensity, extension, probability of occurrence). Finally, it is necessary to integrate the hazard for different return periods with the exposed network to assess the total impact, direct and indirect.