Weighted vulnerability parameters in graphs

Component-based system design comes first among the design approaches used in order to manage the increasing complexity in systems that meet increasing and diversifying requirements. Computer networks and communication systems are component-based designed systems. These systems consist of connected and interoperable components and can be modeled by graph theory. In a computer or communication network, functional losses that may occur as a result of the exposure of components to various effects are defined as vulnerability. Considering the importance of these networks in our lives, the measurement of vulnerability in order to calculate their durability emerges as an important problem. In this thesis; In order to increase the performance of the vulnerability measurement in the graphs, two new vulnerability measurement parameters, which we named as Weighted Binding Number (𝑏𝑖𝑛𝑑௩௪) and Weighted Average Binding Number (𝑏𝑖𝑛𝑑௔௩௪), were defined by examining the currently defined Binding Number (𝑏𝑖𝑛𝑑௩) and Average Binding Number (𝑏𝑖𝑛𝑑௔௩) parameters in the graphs. The software that calculates the newly defined and existing defined parameters is coded with Python language, and the algorithm and pseudo code of the software are given. 𝑏𝑖𝑛𝑑௩, 𝑏𝑖𝑛𝑑௔௩, 𝑏𝑖𝑛𝑑௩௪ and 𝑏𝑖𝑛𝑑௔௩௪ values were calculated for the Data Set (DS96), which includes different types of graphs, and the performances of the newly defined and existing parameters were evaluated based on the results. Keywords: Graph Theory, Vulnerability, Vulnerability Measurement, Binding Number, Average Binding Number, Weighted Binding Number, Weighted Average Binding Number