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# 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 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.