# 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.

`edge_kcomponents` : algorithms for finding k-edge-connected components `connectivity` : algorithms for determining edge connectivity.

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

 Generates nodes in each maximal k-edge-connected component in G. Generates nodes in each maximal k-edge-connected subgraph in G. Finds all bridge-connected components G. 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

 Auxiliary digraph for computing flow based edge connectivity Creates a directed graph D from an undirected graph G to compute flow based node connectivity.