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A problem of finding the maximum feasible flow that can be sent through a network from a source to a sink node while respecting capacities of all edges.

A problem to determine the smallest set of edges that, if removed, would disconnect the source node from the sink, thus minimizing the total flow possible.

An implementation of the Ford-Fulkerson method that uses the shortest augmenting paths, leading to a time complexity of $O(VE^2)$ for $V$ vertices and $E$ edges.

An algorithm for computing maximum flow in a network graph by repeatedly finding blocking flows in a level graph, has a time complexity of $O(V^2E)$.

It maintains a preflow and attempts to locally push excess flow until reaching valid flow, with time complexity $O(V^3)$ for $V$ vertices.

A pivot-based method, much like the simplex method in linear programming, but for solving minimum-cost flow problems on networks.

A constraint that limits the amount of flow that can enter or leave any given vertex in a network, as opposed to just the edges.

The total amount of flow that leaves the source node (or equivalently enters the sink node) in a network flow problem.

A principle stating that the sum of flow into a node should equal the sum of flow out of the node, for every node except the source and sink.