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# Flows

## Maximum Flow

`maximum_flow`(flowG, _s, _t[, capacity, ...]) | Find a maximum single-commodity flow.
`maximum_flow_value`(flowG, _s, _t[, ...]) | Find the value of maximum single-commodity flow.
`minimum_cut`(flowG, _s, _t[, capacity, flow_func]) | Compute the value and the node partition of a minimum (s, t)-cut.
`minimum_cut_value`(flowG, _s, _t[, capacity, ...]) | Compute the value of a minimum (s, t)-cut.

## Edmonds-Karp

`edmonds_karp`(G, s, t[, capacity, residual, ...]) | Find a maximum single-commodity flow using the Edmonds-Karp algorithm.

## Shortest Augmenting Path

`shortest_augmenting_path`(G, s, t[, ...]) | Find a maximum single-commodity flow using the shortest augmenting path algorithm.

## Preflow-Push

`preflow_push`(G, s, t[, capacity, residual, ...]) | Find a maximum single-commodity flow using the highest-label preflow-push algorithm.

## Dinitz

`dinitz`(G, s, t[, capacity, residual, ...]) | Find a maximum single-commodity flow using Dinitz' algorithm.

## Boykov-Kolmogorov

`boykov_kolmogorov`(G, s, t[, capacity, ...]) | Find a maximum single-commodity flow using Boykov-Kolmogorov algorithm.

## Gomory-Hu Tree

`gomory_hu_tree`(G[, capacity, flow_func]) | Returns the Gomory-Hu tree of an undirected graph G.

## Utils

`build_residual_network`(G, capacity) | Build a residual network and initialize a zero flow.

## Network Simplex

`network_simplex`(G[, demand, capacity, weight]) | Find a minimum cost flow satisfying all demands in digraph G.
`min_cost_flow_cost`(G[, demand, capacity, weight]) | Find the cost of a minimum cost flow satisfying all demands in digraph G.
`min_cost_flow`(G[, demand, capacity, weight]) | Returns a minimum cost flow satisfying all demands in digraph G.
`cost_of_flow`(G, flowDict[, weight]) | Compute the cost of the flow given by flowDict on graph G.
`max_flow_min_cost`(G, s, t[, capacity, weight]) | Returns a maximum (s, t)-flow of minimum cost.

## Capacity Scaling Minimum Cost Flow

`capacity_scaling`(G[, demand, capacity, ...]) | Find a minimum cost flow satisfying all demands in digraph G.