Finding the biconnected components of a graph

## Usage

biconnected_components(graph)

## Arguments

graph

The input graph. It is treated as an undirected graph, even if it is directed.

## Value

A named list with three components:

no

Numeric scalar, an integer giving the number of biconnected components in the graph.

tree_edges

The components themselves, a list of numeric vectors. Each vector is a set of edge ids giving the edges in a biconnected component. These edges define a spanning tree of the component.

component_edges

A list of numeric vectors. It gives all edges in the components.

components

A list of numeric vectors, the vertices of the components.

articulation_points

The articulation points of the graph. See articulation_points().

## Details

A graph is biconnected if the removal of any single vertex (and its adjacent edges) does not disconnect it.

A biconnected component of a graph is a maximal biconnected subgraph of it. The biconnected components of a graph can be given by the partition of its edges: every edge is a member of exactly one biconnected component. Note that this is not true for vertices: the same vertex can be part of many biconnected components.

articulation_points(), components(), is_connected(), vertex_connectivity()

Connected components articulation_points(), component_distribution(), decompose(), is_biconnected()

## Author

Gabor Csardi csardi.gabor@gmail.com

## Examples


g <- disjoint_union(make_full_graph(5), make_full_graph(5))
clu <- components(g)\$membership
g <- add_edges(g, c(which(clu == 1), which(clu == 2)))
bc <- biconnected_components(g)