The investigation of changes of integrity values after the vertex and edge addition, subtraction and vertex agglomeration operations in networks

Communication networks can be modeled with a graph data model. Determining how resilient these networks are when their centers or connection lines are damaged is very important for network designers. The resilience of a network is also referred to as the network's vulnerability. The vulnerability value of a communication network is defined as "the strength shown by the network until communication is lost due to the disruption of some centers or the connections between these centers." Vulnerability values are calculated using graph theoretical parameters. The first and most well-known graph vulnerability parameter is the network's connectivity value. Subsequently, many graph vulnerability values have been defined. These include the toughness value, scattering value, integrity value, rupture value, binding value, closeness value and residual closeness value. Additionally, neighbor vulnerability values and average vulnerability values based on these parameters have been defined. When we want to enlarge a network (after adding edges and vertices) or shrink a network (after removing vertices and edges, vertex collapse), the question of how the vulnerability parameter values change, and under what conditions they increase, decrease, or remain unchanged, has become significant. In this thesis, an artificial intelligence model has been created to predict the integrity value, which is one of the important vulnerability measures. The results have been compared with the existing dataset. The developed artificial intelligence model has made predictions with high proximity to the real values. The R-squared (R²) score has been calculated as 0.9094. Then, changes in integrity values after adding and removing vertices and edges, and vertex agglomeration operations have been examined. Finally, the results of the thesis study have been presented.