# Connectivity¶

Connectivity and cut algorithms

## Edge-augmentation¶

Algorithms for finding k-edge-augmentations

A k-edge-augmentation is a set of edges, that once added to a graph, ensures that the graph is k-edge-connected; i.e. the graph cannot be disconnected unless k or more edges are removed. Typically, the goal is to find the augmentation with minimum weight. In general, it is not guaranteed that a k-edge-augmentation exists.

See also

`edge_kcomponents`

- algorithms for finding k-edge-connected components
`connectivity`

- algorithms for determening edge connectivity.

`k_edge_augmentation` (G, k[, avail, weight, …]) |
Finds set of edges to k-edge-connect G. |

`is_k_edge_connected` (G, k) |
Tests to see if a graph is k-edge-connected. |

`is_locally_k_edge_connected` (G, s, t, k) |
Tests to see if an edge in a graph is locally k-edge-connected. |

## K-edge-components¶

Algorithms for finding k-edge-connected components and subgraphs.

A k-edge-connected component (k-edge-cc) is a maximal set of nodes in G, such that all pairs of node have an edge-connectivity of at least k.

A k-edge-connected subgraph (k-edge-subgraph) is a maximal set of nodes in G, such that the subgraph of G defined by the nodes has an edge-connectivity at least k.

`k_edge_components` (G, k) |
Generates nodes in each maximal k-edge-connected component in G. |

`k_edge_subgraphs` (G, k) |
Generates nodes in each maximal k-edge-connected subgraph in G. |

`bridge_components` (G) |
Finds all bridge-connected components G. |

`EdgeComponentAuxGraph` |
A simple algorithm to find all k-edge-connected components in a graph. |

## K-node-components¶

Moody and White algorithm for k-components

`k_components` (G[, flow_func]) |
Returns the k-component structure of a graph G. |

## K-node-cutsets¶

Kanevsky all minimum node k cutsets algorithm.

`all_node_cuts` (G[, k, flow_func]) |
Returns all minimum k cutsets of an undirected graph G. |

## Flow-based disjoint paths¶

Flow based node and edge disjoint paths.

`edge_disjoint_paths` (G, s, t[, flow_func, …]) |
Returns the edges disjoint paths between source and target. |

`node_disjoint_paths` (G, s, t[, flow_func, …]) |
Computes node disjoint paths between source and target. |

## Flow-based Connectivity¶

Flow based connectivity algorithms

`average_node_connectivity` (G[, flow_func]) |
Returns the average connectivity of a graph G. |

`all_pairs_node_connectivity` (G[, nbunch, …]) |
Compute node connectivity between all pairs of nodes of G. |

`edge_connectivity` (G[, s, t, flow_func, cutoff]) |
Returns the edge connectivity of the graph or digraph G. |

`local_edge_connectivity` (G, s, t[, …]) |
Returns local edge connectivity for nodes s and t in G. |

`local_node_connectivity` (G, s, t[, …]) |
Computes local node connectivity for nodes s and t. |

`node_connectivity` (G[, s, t, flow_func]) |
Returns node connectivity for a graph or digraph G. |

## Flow-based Minimum Cuts¶

Flow based cut algorithms

`minimum_edge_cut` (G[, s, t, flow_func]) |
Returns a set of edges of minimum cardinality that disconnects G. |

`minimum_node_cut` (G[, s, t, flow_func]) |
Returns a set of nodes of minimum cardinality that disconnects G. |

`minimum_st_edge_cut` (G, s, t[, flow_func, …]) |
Returns the edges of the cut-set of a minimum (s, t)-cut. |

`minimum_st_node_cut` (G, s, t[, flow_func, …]) |
Returns a set of nodes of minimum cardinality that disconnect source from target in G. |

## Stoer-Wagner minimum cut¶

Stoer-Wagner minimum cut algorithm.

`stoer_wagner` (G[, weight, heap]) |
Returns the weighted minimum edge cut using the Stoer-Wagner algorithm. |

## Utils for flow-based connectivity¶

Utilities for connectivity package

`build_auxiliary_edge_connectivity` (G) |
Auxiliary digraph for computing flow based edge connectivity |

`build_auxiliary_node_connectivity` (G) |
Creates a directed graph D from an undirected graph G to compute flow based node connectivity. |