Flows in Networks

Abstract

Graphs are used to model situations in which a commodity is transported from one location to another. A common example is the water supply, where the pipelines are edges, vertices represent water users, pipe joins, and so on. In the example of an airline, given in Section 2.2, we can interpret freight or passengers as commodities to be transported. Highway systems can be thought of as transporting cars. In many examples it is natural to interpret some or all edges as directed (some roads are one-way, water can flow only in one direction at a time in a given pipe, and so on). A common feature of transportation systems is the existence of a capacity associated with each edge — the maximum number of cars that can use a road in an hour, the maximum amount of water that can pass through a pipe, and so on.