## 2 Background
### Graph Theory  
CIs are a highly interrelated and interdependent system, comprising several components, services, and nodes containing crucial information. There are numerous threats and  
Figure 1: Three variable Bayesian network examples.  
risks that may endanger critical data security and privacy in different CIs. After recognizing the CI risks, the next step for the CI safety and security evaluation is to offer an appropriate model for demonstrating the connection among potential risk sources. The GT model represents the study of mathematical structures applied to prototypical pairwise associations between entities, including nodes and points connected by edges or links. For GT analysis, graphs can be divided into various types, comprising of directed and undirected graphs and connected and disconnected charts, as well as weighted, bipartite, and simple graphs. GT analyzed the connectivity properties for susceptibility, trustworthiness, and risk analysis for several applications, i.e., vehicle networks using different graphs [28, 29, 30]. Moreover, topological properties enable techniques, flow-based approaches, and hybrid methods to analyze the reliability, hazards, and safety of systems [31].  
There are several benefits of using the graphs model in different sectors. The first and foremost strength of GT is to describe the topological association between several nodes, connecting links between locations (Figure 2). It helps review the connectivity and the degree distribution of every location in a topological space. Those notions are essential for examining the networks. In the case of a spatial network, the vector and geometric characteristics are incredibly beneficial. Vectors properties provide a directional links; for transportation modeling, this property is applied to model flows between locations. The usage of geometrics properties is to insert distance into the model, allowing spatializing the system in Euclidian space. Moreover, GT also offers a description of relations through the graph. Based on the path, i.e., a course among components into the graph, and cycle (a path with a similar origin and endpoint), these characteristics allow for the study of the relationships between various parts of the charts [32, 33, 34].  
In existing studies, GT has been applied in protecting systems [35]. An undirected graph H = (U, F) represents a mathematical structure, comprising two sets, U and F, where U = {u1, u2,..., um} defines the set of nodes. The set of edges is presented by F = {f1, f2,..., fn}. The undirected graph may be useful in presenting CIs or any other complex systems. Furthermore, each subsystem, such as oil and gas, power, and networks, can be exhibited by a subgraph. In GT, each component of the system represents a link, and the nodes are the connections between components, as per the topology of the network. Interdependencies among subsystems are modeled as definite links between end terminals of the two relevant components or subsystems. The CI graph model is supposed to have m nodes and n connections [36].  
Figure 2: An illustration of graph theory.  
GT has become a critical component in various computing applications, such as CI security and network development. However, it is also among the most challenging areas to comprehend and apply for protecting networks, as well as infrastructures. [PERSON] and [PERSON] discussed GT and its real-time implementation in different threat and vulnerability analyses [37]. [PERSON] et al. discussed the optimization problems associated with GT and its security applications, using GT concepts to characterize various networks, assess network protocols for multiple scenarios in networking and security, and tools used to generate graphs for demonstrating real-world systems [38]. [PERSON] et al. demonstrated GT's applicability in heterogeneous fields but primarily focused on technical applications that utilize theoretical graph notions [39].