Vulnerability of networks against rank ordered independent link failures

Abstract

In this study, various random and regular networks are investigated and compared in terms of their vulnerabilities against independent but ordered failures. Upon the mathematical basis of graph theory, methods of analysis of the structure and topology of networks are investigated, and parameters such as shortest paths, cuts, and degree distributions dealing with connectivity patterns are analyzed. Moreover, probabilities and correlations between the connected elements of networks are defined, measured and compared. Using these parameters, centrality and betweenness measures are discussed as primary methods of ranking and used to rank these elements in terms of specific functions such as network performance and reliability. Failure scenarios based on these ranking methods are applied on ring structures, Erdos Renyi, scale free and small world networks as well as Istanbul’s highway and rapid transit networks and Turkish railway network. The responses of these networks against these failures are shown to be related to their structural properties and topologies.