*In **graph theory**, a flow network (also known as a transportation network) is a *

*directed graph*

*where each edge has a*

**capacity**and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in*operations research*

*, a directed graph is called a*

**network**, the vertices are called**nodes**and the edges are called**arcs**. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a**source**, which has only outgoing flow, or**sink**, which has only incoming flow. A network can be used to model traffic in a road system, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes.**NSI**is applying analogies and results from communication networks design and analysis to transportation networks.