cant concern is that telecommunications networks tend to be two-way rather than one-way. It is theoretically feasible to model these flows as two different networks, although if the capacity of certain nodes is used for traffic passing in both directions, some means for trading off capacity must be devised. The problem can also be analyzed as a multicommodity flow problem. Multicommodity problems pose additional difficulties that sometimes border on the intractable (Stein 2004). Networks in Telecommunications Figure 2.6. Illustration of the max-flow/min-cut theorem This insight is most easily understood by analyzing the simplest cuts in the context of the relatively simple network depicted in Figure 2.6. That network consists of eight nodes connected by a series of links; the capacity of each link is indicated on the graph. 5 Consider the cut represented by the dotted line labeled A. In this cut, which consists of the links connecting node S to nodes a, b, and f, set S consists of only node S, whereas set T consists of the remaining seven nodes (a, c, d, e, f, and t). Any traffic leaving node S must necessarily travel along one of the links connecting node S to node a, b, or f. As a result, it is clear that the total carrying capacity of the network from S to t can be no greater than the sum of the capacity of those links, which in this case is 38 + 1 + 2 = 41. A similar logic obtains with respect to cut B, which divides the network into a set S consisting of seven nodes a, b, c, d, e, and f) and a set T consisting only of node t. Because only four links connect to node t, it is also clear that the total capacity of the network cannot exceed the total capacity of those four links (which in this case is 7 + 7 + 1 + 18 = 33). Because every traffic flow must necessarily pass through both of these cuts, the capacity of the links crossing these cuts represents a constraint on the flow capacity of the entire system. In other words, the network cannot possibly carry more than the lower of 41 or 33. One can generalize fr