# 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.