Editing Flow network (section)

==Applications==
{{see also|Pipe network analysis}}
{{Unreferenced section|date=June 2023}}

Picture a series of water pipes, fitting into a network. Each pipe is of a certain diameter, so it can only maintain a flow of a certain amount of water. Anywhere that pipes meet, the total amount of water coming into that junction must be equal to the amount going out, otherwise we would quickly run out of water, or we would have a buildup of water. We have a water inlet, which is the source, and an outlet, the sink. A flow would then be one possible way for water to get from source to sink so that the total amount of water coming out of the outlet is consistent. Intuitively, the total flow of a network is the rate at which water comes out of the outlet.

Flows can pertain to people or material over transportation networks, or to electricity over [[electrical distribution]] systems. For any such physical network, the flow coming into any intermediate node needs to equal the flow going out of that node. This conservation constraint is equivalent to [[Kirchhoff's current law]].

Flow networks also find applications in [[ecology]]: flow networks arise naturally when considering the flow of nutrients and energy between different organisms in a [[food web]]. The mathematical problems associated with such networks are quite different from those that arise in networks of fluid or traffic flow. The field of ecosystem network analysis, developed by [[Robert Ulanowicz]] and others, involves using concepts from [[information theory]] and [[thermodynamics]] to study the evolution of these networks over time.