ng a single central hub and the total cost of establishing two peripheral hubs. Also, for ease of discussion, suppose that the cost of reaching a peripheral hub is negligible. The cost of a link in the star network is a. The variable cost per final customer of the trunk line is C regardless of where the customers are located. The trunk line has a fixed cost of F. As the number of total customers gets large, the two-hub configuration becomes desirable. The critical number of customers, given that a > C, is As long as n is greater than or equal to the value n*, the network designer will choose a two-hub configuration. The two choices are represented in Figure 2.5. Even though the two alternative networks appear modular, it should be clear that the optimal network design is sensitive to the costs of individual network elements and to the number of potential customers. For example, suppose that the cost of a link in the star network is a = 20 and the variable cost per customer of the trunk line is C = 15. Suppose that the fixed cost of the trunk line is 48. Then the trunk- line network only becomes attractive if there are 10 or more customers. The Design and Costs of Networks Suppose that a regulator were to require the addition or removal of terminal nodes through unbundled access. This would affect which network configuration was optimal because the number of terminal nodes affects the cost of each design. This conclusion applies generally to more complex types of networks and different cost structures. 5. The Max-Flow/Min-Cut of a Network In addition to providing insights into how the interrelationships among particular network components affect the network's overall cost and reliability, graph theory also reveals how network configuration affects the network's maximum capacity. This section introduces a well-known principle in graph theory known as the max- flow/min-cut theorem, which provides a way to determine the maximum carrying capacity of any transportation network and the costs associated with operating it