# biconnected_components: Biconnected components In igraph: Network Analysis and Visualization

## Description

Finding the biconnected components of a graph

## Usage

 `1` ```biconnected_components(graph) ```

## Arguments

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

## 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.

## 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`.

## Author(s)

Gabor Csardi csardi.gabor@gmail.com

`articulation_points`, `components`, `is_connected`, `vertex_connectivity`
 ```1 2 3 4``` ```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) ```