  The maintenance of system flow is critical for effective network operation.
Any type of disruption to network facilities (arcs/nodes) potentially risks
loss of service, leaving users without access to important resources. It is
therefore an important goal of planners to assess infrastructures for
vulnerabilities, identifying those vital nodes/arcs whose debilitation would
compromise the most source-sink (s-t) interaction or system flow. Due to the
budgetary limitations of disaster management agencies, protection/fortification
and planning for the recovery of these vital infrastructure facilities is a
logical and efficient proactive approach to reducing worst-case risk of service
disruption. Given damage to a network, evaluating the potential for flow
between s-t pairs requires assessing the availability of an operational s-t
path. Recent models proposed for identifying infrastructure vital to system
flow have relied on enumeration of all s-t paths to support this task. This
paper proposes an alternative model constraint structure that does not require
complete enumeration of s-t paths, providing computational benefits over
existing models. To illustrate the model, an application to a practical
infrastructure planning problem is presented.
