Evaluating network importance measures based on the construction spectrum

The construction spectrum is a useful tool to investigate the network reliability, which only depends on network structure and is called structure invariant. Importance measures are efficient tools to quantify and rank the impact of edges within a network. This study considers the K-terminal network with n edges and assumes that edges fail with an equal probability. The article focuses on investigating the importance measures of individual edge for the K-terminal network, including reliability achievement worth and reliability reduction worth, via the construction spectrum–based method. Generally, we establish the equations for reliability achievement worth and reliability reduction worth using the construction spectrum and determine the conditions under which the importance rankings generated by reliability achievement worth and reliability reduction worth only depend on the network structure through the construction spectrum. Similar results are obtained with reliability achievement worth and reliability reduction worth for pair of edges. A construction spectrum–based Monte-Carlo simulation is used to estimate reliability achievement worth and reliability reduction worth. Finally, a numerical example is presented to illustrate the application of these measures.