 of specialized equipment are installed and perform various tasks. Thus, in a communications network, switching takes place at the nodes, and equipment for transmission and reception of information also is located at terminal nodes. 5 The terms nodes and links are analogous to the terms vertices and edges that appear in much of the literature on graph theory. Networks in Telecommunications Figure 1.2. The set of nodes is {1, 2, 3, 4}. The set of links is {(1,2), (1,3), (1, 4), (3, 4)}. In a network that is tied to a specific location, such as a railroad or an electrical system, nodes indicate geographic locations for junctures and switching equipment, such as the location of a train station in a railroad or a central office switching station in a telecommunications system. However, generally nodes need not be confined to a specific location. Mobile phones are among the nodes of a wireless network, SO that nodes can move around while still being part of a network. Nodes can even jump from one network to another, as occurs when mobile phones roam across different wireless networks, or laptop computers with radio transmitters move into and out of WiFi networks. A link in a network is any type of connection between nodes. Links can be fixed in place, such as electrical transmission lines or fiber-optic communication lines. Links can be flexible and temporary, such as the airplanes and routes that form the links of an airline system, because such links can be created or terminated by the managers of the airline. Links need not represent specific geographic corridors. For example, a transmitter within a wireless phone network may be in a specific geographic location, but the communication links with mobile phones depend on the location of the phones. The structure of a network can be represented using a graph that provides a picture of the network A. Graph G is composed of two sets. The first set in a graph is a list of the nodes of the network, which we label consecutively for convenience. For a network with n nodes, 