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. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, except when it is a source, which has more outgoing flow, or sink, which has more incoming flow.
Often in Operations Research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs.
From West's Introduction to Graph Theory's Appendix D Glossary and Terms
Network : a directed graph with a distinguished initial vertex (source) and a distinguished, terminal vertex (sink), in which each edge is assigned a flow capacity and possibly also a flow demand (lower bound).
So I wonder what the definition for a network is?
Must a network be directed? Both sources said so, but from my past intuition, a network can be undirected.
- Must a network have a weight or flow for each edge? Must a network have a capacity on the weight or flow for each edge? Wikipedia seems say no and only flow networks can have them, while West seemed to say yes.
- Must a network have a source vertex and a sink vertex? Wikipedia seems say no and only flow networks can have them, while West seemed to say yes.
I understand that there may be different definitions by different people, including those not listed here. However, I would like to know what definition makes more sense and/or receives more consensus?