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What is flow in context of minimum-cost network? I know that a minimum cost network is a directed graph G={V,E}, where each edge has a cost and capacity value. The problem is to find best 'path' to send d amount of flow from source to terminal node so that the total cost is minimized. My question is: what does flow denotes?

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Flow is an abstraction of how much "stuff" you want to move through the network. Exactly what the stuff is depends on what you're modelling with the network - water pipes, transport networks, computer networks, etc.

The problem (or something close to it) can also be used to model other problems, in which case flow could be all kinds of things.

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