## 3 Methodology
### Description of Network Functionality and Network Contingency Quantification
In such models, nodes signify the various components of the grid, and edges represent the inter-relationships between them. Through these AG-based models, it is possible to swiftly identify the primary causes of an outage. Furthermore, they provide a roadmap for an effective response strategy to restore either power grids, as discussed in [33], or data networks, as highlighted in [34]. AG showcases the dependencies present within the system, allowing for the identification of pivotal elements integral to the full functionality of the system. In principle, an oriented AG, as the represented system, is structured through nodes and edges, but the implications of nodes and edges in the context of a graph significantly differ from general interpretations. Figure 4: Diagram of interconnected infrastructures simplified by omitting the elements without direct influence on the defined system function. In this case, there is a comprehensive breakdown of the interpretation of these nodes and edges in accordance with [26]:  
* First, the graph is inherently acyclic, ensuring that two directly connected nodes share a singular edge. * At the top of the AG is a solitary SS node. This unique node symbolizes the overall system's functionality, illustrating correct operation against system failure. * An inherent directionality exists between the nodes of the AG, establishing the relationship of subordination between them, delineated as a slave node in relation to a master node. * An internal node, also referred to as a non-terminal node, typifies the stochastic behavior inherent within a subsystem. This subsystem is perceived to be in a state of correct functionality only when a minimum of \(m\) subordinate nodes (which can either be terminal or non-terminal) concurrently display correct functionality. This stipulation requires the integer \(m\) to reside within a specific interval. Specifically:
* The total number of input edges is marked \(n\). * For a situation where \(m\) equals 1, the internal node effectively emulates a logical OR function. * Conversely, when \(m\) matches \(n\), the internal node resonates with a logical AND function. * The role of terminal nodes is pivotal as they symbolize the operational status of the diverse components integrated within the system. To be precise, these components are subject to events which can either be stochastic in nature or deterministic. For those events characterized by stochasticity, they need to be articulated via distinct probability distributions, specifically catering to the occurrence of faults. Additionally, events tethered to maintenance, either preventive or corrective, necessitate clear and unambiguous specifications. In the presented case, Node S1 therefore indicates the state where this POD in Figure 4 is supplied. Components that are essential to this state of operation include the C4 cable, the T1 power transformer, and the DT2 distribution transformer. Furthermore, ensuring consistent functionality is a supply pathway, including both lines and LBS. An illustrative representation of the power grid's structure is shown in Figure 5.  
In the test network, as depicted in Figure 4, a similar procedure is administered to the communication segment, which is highlighted in blue. Taking into account the interdependencies between the two infrastructures in the comprehensive test network, the system's functional correctness is delineated as facilitating LBS oper  
Figure 5: AG of the power grid part of the simplified test network. Center from the power component of the network. As such, in Figure 4, the pertinent segment of the communication network is emphasized in blue, playing an indispensable role in powering the aforementioned LBS component. Other elements are deemed non-essential for the AG design. The AG tailored for the communication segment of the network, developed in line with the outlined procedure, is illustrated in Figure 6. In this context, solely the interdependencies amidst the constituents of the communication segment are represented within this AG.