Networks are illustrated as diagrams consisting of two main components: nodes and branches. Nodes represent junction pointsfor example, an intersection of several streets . Branches connect the nodes and reflect the flow from one point in the network to another. Nodes are denoted in the network diagram by circles , and branches are represented by lines connecting the nodes. Nodes typically represent localities, such as cities, intersections, or air or railroad terminals; branches are the paths connecting the nodes, such as roads connecting cities and intersections or railroad tracks or air routes connecting terminals. For example, the different railroad routes between Atlanta, Georgia, and St. Louis, Missouri, and the intermediate terminals are shown in Figure 7.1.
Figure 7.1. Network of railroad routes
Nodes , denoted by circles, represent junction points connecting branches .
Branches , represented as lines, connect nodes and show flow from one point to another.
The network shown in Figure 7.1 has four nodes and four branches. The node representing Atlanta is referred to as the origin , and any of the three remaining nodes could be the destination , depending on what we are trying to determine from the network. Notice that a number has been assigned to each node. Numbers provide a more convenient means of identifying the nodes and branches than do names . For example, we can refer to the origin (Atlanta) as node 1 and the branch from Atlanta to Nashville as branch 12.
Typically, a value that represents a distance, length of time, or cost is assigned to each branch. Thus, the purpose of the network is to determine the shortest distance, shortest length of time, or lowest cost between points in the network. In Figure 7.1, the values 4, 6, 3, and 5, corresponding to the four branches, represent the lengths of time, in hours, between the attached nodes. Thus, a traveler can see that the route to St. Louis through Nashville requires 10 hours and the route to St. Louis through Memphis requires 8 hours.
The values assigned to branches typically represent distance, time, or cost .