# 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.