Measuring the vulnerability in networks via link residual closeness

A network is composed of processing nodes and communication links between these nodes. In a network, vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. A variety of parameters have been proposed to measure the vulnerability of a network modeled by a graph including connectivity and edge-connectivity, toughness and edge-toughness, scattering number and edge-scattering number, integrity and edge-integrity, tenacity and edge-tenacity, rupture degree and edge-rupture degree. Vertex residual closeness and link residual closeness are novel parameters defined as network vulnerability measures. In this thesis, firstly it is pointed out that link residual closeness is more sensitive as a measure of graph vulnerability than the other vulnerability measures existing in literature and the need and advantages of the parameter are stated. Then, link residual closeness of specific types of graphs, path and wheel related graphs and graph operations are evuluated. Finally, a polinomial time algorithm based on Floyd-Warshall algorithm is proposed to determine the link residual closeness of a graph.