om this insight by analyzing the entire universe of possible cuts to the network. The cut with the smallest capacity (called the minimum cut) represents the maximum flow that one can push through the system. 6 The 5 Figure 2.6 is adapted from Jungnickel (1999). 6 Although it is quite intuitive that the maximum carrying capacity of a transport network must be less than or equal to the capacity of the minimum cut, the max-flow/min-cut theorem actually establishes that the maximum flow of the network is strictly equal to the capacity of the minimum The Design and Costs of Networks Figure 2.7. Impact of unbundled access on network capacity. minimum cut in any network can be identified using an iterative algorithm. In this case, the cut with the minimum capacity is the one depicted by cut C, which has a capacity of 31. Because all traffic traveling between nodes S and t must necessarily travel across cut C, the total capacity of the links crossed by cut C necessarily rep- resents the maximum carrying capacity of the network. In addition, the algorithm for identifying the minimum cut also determines the flow passing along each non- critical link when the network is operating at full capacity. This makes it possible to determine the direct cost of operating the network when it is carrying its maximum volume.7 Now consider the impact on the network of granting a competitor access to a network element. Access ties up some of the capacity of the leased elements, which in turn reduces the capacity available to the network owner. One of the most interesting insights of graph theory is that changing the capacity of any particular network component can have a surprising and somewhat unpredictable impact on the capacity of the network. Indeed, changes in capacity can cause the links that compose the minimum cut (which represents the constraint on the total carrying capacity of the network) to change to a completely different set of links. Consider, for example, the situation depicted in Figure 2.7, which is the same network rep