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This paper provides an overview of some of the recent developments in the assessment of network vulnerability and robustness through appropriate tools that assist in the quantification of network efficiency / performance and the identification of the importance of network components, such as nodes and links. We demonstrated how rigorously constructed and well-defined network measures can capture not only the network topology underlying a particular critical system, but also the underlying behavior of decision-makers, the resulting flows, and induced costs in the reality of demands for resources, whether fixed or elastic (price-dependent). In addition, we reviewed how to determine the synergy associated with network integration, with a focus on supply chains, as may occur not only in corporate applications, such as in mergers and acquisitions, but also in humanitarian ones, as in the case of the creation of teams and partnerships for humanitarian logistics.We illustrated the concepts and tools in this paper, which are based on numerous publications, through a spectrum of applications and numerical examples. Since the number of disasters is growing globally, it is imperative to have transparent, well-understood, and appropriate tools for the determination of network vulnerability and robustness, since critical infrastructure networks from transportation, telecommunications, supply chains, to financial and electric power ones, provide the ties that bind our economies and societies together. Local disruptions can have global impacts. Only when network components are identified as to their importance and rankings can decision-makers and policy analysts as well as planners and engineers understand in an objective way which components should be maintained and 1 protected the most with implications for disaster and emergency preparedness as well as national security.

In this paper, we propose a network efficiency measure for congested networks, that captures demands, costs, flows, and behavior. The network efficiency/performance measure can identify which network components, that is, nodes and links, have the greatest impact in terms of their removal, due to, for example, natural disasters, structural failures, terrorist attacks, etc., and, hence, are important from both vulnerability as well as security standpoints. The new measure is applied to the Braess paradox network in which the demands are varied over the horizon and explicit formulae are derived for the importance values of the network nodes and links. This measure is applicable to such congested networks as urban transportation networks and the Internet.

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