The Max-Flow Min-Cut Theorem states that in a flow network, the maximum value of flow from a source to a sink is equal to the total weight of the edges in the smallest cut that separates the source and sink. This theorem provides a powerful way to analyze network flow problems, ensuring that the flow is optimal and no more flow can be achieved without increasing the capacity of the network or changing its structure.

Max-Flow Min-Cut Theorem

A flow network is a directed graph where each edge has a capacity and each flow must not exceed the capacity, typically used to model the flow of resources through a system. The goal is often to find the maximum flow from a source node to a sink node, which can be efficiently computed using algorithms like the Ford-Fulkerson method.

flow network

maximum value of flow

Source to sink

total weight of the edges

smallest cut

analyze network flow problems

Optimal flow

Increase the capacity of the network

changing its structure

Fundamental Principles of Network Coding

Relevant Degrees

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