Affiliations: Faculty of Engineering and Computer Sciences, Izmir University of Economics, 35330, Izmir, Turkey. zeynep.odabas@ieu.edu.tr | Department of Mathematics, Faculty of Science, Ege University, 35100, Izmir, Turkey
Note: [] Address for correspondence: Faculty of Engineering and Computer Sciences, Izmir University of Economics, 35330, Izmir, Turkey
Abstract: Networks are known to be prone to node or link failures. A central issue in the analysis of networks is the assessment of their stability and reliability. The main aim is to understand, predict, and possibly even control the behavior of a networked system under attacks or disfunctions of any type. A central concept that is used to assess stability and robustness of the performance of a network under failures is that of vulnerability. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Different approaches to properly define a measure for graph vulnerability has been proposed so far. In this paper, we study the vulnerability of cycles and related graphs to the failure of individual vertices, using a measure called residual closeness which provides a more sensitive characterization of the graph than some other well-known vulnerability measures.
Keywords: Graph vulnerability, Closeness, Network design and communication, Stability, Communication network, Cycles
