3.4 Routes Through Networks
The second set of network location problems are fixed point in the sense that all junctions are confined to the nodes or cities to be connected. We describe them here under the title of routes through networks since designing the network may be more simply regarded as selecting one particular configuration from the very large (but finite) range of possible networks Before proceeding with our discussion, we define the following terms which are used to describe networks made up of n points or nodes joined by r links. A link is simply a line connecting two points, and a Hamiltonian circuit is a sequence of links which forms an unbroken chain passing through all the n points, and in which the first and last points coincide. The travelling salesman tour is the shortest Hamiltonian circuit. A spanning tree is a collection of n-1 links joining the n points, such that any point can be reached from any other point. The minimal spanning tree is the shortest of all such spanning trees