Network Efficiency Measurement and Vulnerability

In a major study, funded by the National Science Foundation, under the “Management of Knowledge Intensive Dynamic Systems” (MKIDS) program, John F. Smith Memorial Professor Anna Nagurney and an Isenberg School of Management doctoral student, Qiang “Patrick” Qiang, have developed a computer-based tool to identify the most vulnerable nodes and links in critical infrastructure networks ranging from transportation networks to electric power supply chains and financial networks. The new tool is a network efficiency measure that captures the demand for network resources based on user behavior and associated costs and flows and enables the computation of the loss in efficiency if network components such as nodes or links (or combinations) are destroyed. Failures of network components, be they roads, bridges, electric power stations, transmission lines, etc., can occur due to natural disasters, structural breakdowns, accidents, or terrorist attacks. The network efficiency measure generalizes a previously proposed network efficiency measure that focused on distance between nodes (or points) in a network and had been applied to the Internet and the Boston subway system. The new network efficiency measure captures how users of the network (be they drivers, financial investors, or electric power flows) dynamically readjust after the network disuptions. Hence, decision-makers and policy analysts can now, with the new tool, identify the most critical nodes and links in a network (and their rankings). The most critical network components should be most protected from a security standpoint since their removal will result in the greatest loss to network efficiency.

“We are very excited about our new network efficiency measurement tool which allows for the identification of the most important nodes and links in network systems that are essential to US prosperity and national security,” says Professor Anna Nagurney. “We expect that the measure will have wide practical use also in peacetime since it provides a quantifiable way in which to identify which network components should be best maintained based on actual usage and costs.”

The first results of the study have been accepted for publication in the journal Optimization Letters under the title, “A Unified Network Performance Measure with Importance Identification and the Ranking of Network Components.” A preprint is available at:

For more information, contact: Dr. Anna Nagurney
John F. Smith Memorial Professor and Director
Virtual Center for Supernetworks
Isenberg School of Management
University of Massachusetts
Amherst, MA 01003
Phone: 413-545-5635
Center site:

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