y to the usual pictures of the nodes as "dots" and the arcs as "lines" between them, but this representation allowed us to use graph-theory methods to re- duce maintenance expenses. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Capacity Calculations for Cellular Networks Capacity and Quality Principles Figure 26.2 Star graph showing separate backhaul links. Figure 26.3 Complete graph of link possibilities. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Capacity Calculations for Cellular Networks Capacity Calculations for Cellular Networks airports and arcs are airline flight routes, then the complete graph represents a full schedule, and the star graph represents the hub-and-spoke pattern. The third type of graph that interests us is a tree graph, a graph that has exactly one way to get from any node to any other node along the arcs. In a tree graph, we can pick any node as a root, and the arcs form a fan-out from that root. If the backhaul network is a tree graph, then we can make the MSC node the root of the tree SO that the arcs of the graph are the backhaul links in use. Another feature of a tree graph is that it has no cycles, no sequences of distinct arcs that end up where they start. 26.1.3 Network flow optimization There is a class of graph-theory optimization problems called network flow problems. These problems have a specific structure that makes them particularly attractive computer-solving algorithms. Some network flow formulations are apparent, such as maximization the flow of something through some sort of network. Other model for- mulations are more subtle, where the nodes, arcs, and flows are mathematically sym- bolic representations of physical enti