Total Weighted Value (*TWVI I*)

Combining the three centrality metrics forward beside the power requirements, we define a total weight value for interconnected infrastructure *TWVI I*(*v*) for each node *v* ∈ *V*(*G*). In calculating *TWV*, feature scaling [24] is used to bring all values into a common range by applying the *z*-*score* normalization approach based on the mean and standard deviation of each node metric across all nodes *v* [25], as shown for metric *Cd*(*v*):

$$\mathbb{C}\_{d\_{norm}} = \frac{\mathbb{C}\_d(v) - mean(\mathbb{C}\_d(v))}{standard \, deviation(\mathbb{C}\_d(v))} \tag{4}$$

We apply the normalization method to each metric, resulting in the following:

$$TPV\_{II}(\upsilon) = \mathbb{C}\_{d\_{norm}}(\upsilon) + \mathbb{C}\_{b\_{norm}}(\upsilon) + \mathbb{C}\_{\varepsilon\_{norm}}(\upsilon) + \mathbb{C}\_{p\_{norm}}(\upsilon) \quad . \tag{5}$$

### 2.2.2. Standalone Infrastructure

Many critical infrastructures are not typically presented as a graph (e.g., factories and healthcare). Instead, as standalone infrastructures, we utilize a weighted mixture of *m* context-dependent factors to discover the related importance of infrastructure elements. For instance, the characteristic factors of one healthcare element, such as a hospital, are the capacity of that hospital in terms of power requirements, bed number, and the population inhabited around the hospital.

Four critical infrastructures have been measured in this paper, as follows:

### Healthcare

A healthcare infrastructure analysis has shown that hospitals are the most critical components. Therefore, ensuring that hospitals are running is crucial to disaster response and resilience. Accordingly, three parameters were employed to describe hospitals: (1) power consumption, (2) capacity, and (3) population surrounding a hospital area. Hospital size or capacity is typically determined through a specific quantity of beds that can be obtained from publicly available information. Employing the same hospital capacity further points

to a helpful parameter called energy consumption over applying the formula conducted by Schneider Electric [26], as

$$P\_H = BD \ast \mathcal{U} \tag{6}$$

This equation represents the hospital energy use as *PH*, *BD* denotes the number of operated beds in the same hospital, and *U* signifies the bed's power use in kWh (assumed as 30,000 kWh/year in [26]). The population surrounding the hospital is another parameter assigned to measure the importance of healthcare nodes. It can be assigned using the density data from [27] and a one km radius circular space throughout that node (hospital).

### Water System

Through natural disasters, ensuring a reserve of drinking water is crucial. Therefore, water treatment plants have been selected to be critical in this model to ensure the supply of such infrastructures. Their size can also be characterized by millions of gallons per day (MGD). Thus, the power consumption *PW* was also estimated utilizing the following formula:

$$P\_W = G \ast J \tag{7}$$

*G* in this equation reflects the portion of water processed in the MGD unit, and *J* represents the power required to process a million gallons [28], where the average water planet use around 1470 kWh/MG.

### Cellular Network

The communication infrastructure is considered one of the most vital infrastructures to a society remaining functional. Due to the ubiquity of cell phones, cellular base stations are considered significant elements in the communication infrastructure. Furthermore, the authors of [9] discussed how the cellular network could be reconfigured to be used to provide disaster recovery communications. This study identified the most critical cellular network base stations by employing three factors: (1) geographic coverage, (2) population covered, and (3) power requirements. The geographic coverage for each base station was classified into short, medium, and long in terms of distance in miles.

### Emergency Shelter

Through natural disasters, it is critical to provide emergency shelters with power. Governments commonly utilize event centers as a shelter when emergencies occur. For instance, the George R. Brown Convention Center in Houston, TX, covered thousands of people throughout hurricane Harvey [29]. Three inputs were selected to classify emergency shelters: energy usage, size, and capacity. Both data regarding the capacity and size of emergency shelters are openly accessible online. Nevertheless, power consumption was determined by calculating the size in *f t*<sup>2</sup> and then by multiplying it by the power average required for universal non-residential property space, which is 14 kWh per *f t*<sup>2</sup> [30].
