Some vulnerability parameters and algorithms in weighted graphs

Vulnerability in networks and reliability of networks are important issues in many areas. Vulnerability is expressed as the endurance power of the devices in a network until their communication is broken in case of any disruptions in their connections. In order to make vulnerability measurements, it is necessary to model it with graphs and to benefit from vulnerability parameters. In the scope of this thesis, scattering number, which is one of the vulnerability measurement parameters, was discussed. Scattering number and average scattering number calculations for an unweighted graph and the related applied code were prepared. Time complexity was calculated for this modeled structure. In the scope of this article, average scattering number calculation algorithms in weighted graphs, applied project and result tables were given and worked on. In addition, the complexity value of the prepared algorithm was calculated. While calculating the average scattering number in the weighted graph, ScvW(G) =max{c(G − Sv) − w|Sv|, c(G − Sv) ≥ 2} was defined. The weight values of the values that are removed in addition to the scattering number calculation are taken into account. As a result, the definition of the average scattering number in the weighted graph will be scavw(G) =(∑(v∈V(G))〖scv w(G) 〗)/n. In this study, general results, definitions, theorems and time complexity for the average number of scatters in Weighted Graphs, which were not previously available in the literature, were included. It was analyzed with shared algorithm and code criteria.