Summary of Module

This module introduces the reader to the vulnerability analysis of a transportation system by modeling it using graphs or networks. Basic definitions and concepts from graph theory are introduced. Measures of node centrality are defined and illustrated. Using these concepts, hypothetical transportation systems are modeled and analyzed for their vulnerability to a failure or an attack. In the event of the disruption of a station or pathway, the consequences are quantified in terms of an increase in travel time or a reduction in the network capacity.

Note to teachers: Solutions to exercises appear in red in the module.

Target Audience  

This module is written for undergraduate students in a freshman/sophomore level course in mathematics, engineering or environmental science.  

Prerequisites

Students should be prepared for college level mathematics.

Topics

The topics in this module include graphs, transportation networks, measures of centrality, modeling transportation disruption, cost and loss of capacity.

Goals

Our goal is to introduce the student with minimal background to modeling a threat to a transportation network.

Anticipated Number of Meetings

2-3 Class periods:

• 1 class period for covering background material for graphs and measures for centrality.
• 1 class period for modeling transportation disruptions.
• 1 class period for further researching a topic of interest or constructing a model for a local transportation network.

Learning Outcomes

Students completing this module will be able to:

• Give definitions for and illustrations of basic graph theory concepts including: graph, node, edge, order, size, degree, neighborhood, path, distance, geodesic, bridge and cut-node
• Interpret a transportation system modeled as a graph.
• State and apply the definitions of measures of centrality of nodes such as degree centrality and closeness centrality.
• Apply the centrality measures to a transportation network modeled as a graph.
• Analyze a disruption to a transportation network modeled by a graph.