Approach

A network is a collection of nodes and links. Networks are useful for modeling real-life systems; for example, a network may be used to model highways, where nodes are intersections, and links are the roads between intersections.

A path is a series of contiguous nodes on a network. There may be many paths on a network. Each path starts at an origin node, passes through intermediate nodes, and ends at a destination node. Paths may overlap, so multiple paths share a certain sub-sequence of nodes.

Each path has a flow, which is a number. In the highway application it may be the number of vehicles traveling on that path in an hour. Often the path flows are not directly observable. For example, we can count the number of vehicles traveling a single link (road segment); but because paths can overlap, those vehicles could be traveling on multiple paths, and we cannot tell how many vehicles are traveling on each.