# biconnected.components

From igraph v0.5.3
by Gabor Csardi

##### Biconnected components

Finding the biconnected components of a graph

- Keywords
- graphs

##### Usage

`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. components The components themselves, a list of numeric vectors. Each vector is a set of edge ids giving the edges in a biconnected component. articulation_points The articulation points of the graph. See `articulation.points`

.- See examples below on how to extract the vertex ids of the biconnected components from the result.

##### concept

Biconnected component

##### See Also

`articulation.points`

, `clusters`

,
`is.connected`

, `vertex.connectivity`

##### Examples

```
g <- graph.disjoint.union( graph.full(5), graph.full(5) )
clu <- clusters(g)$membership
g <- add.edges(g, c(which(clu==0), which(clu==1))-1)
bc <- biconnected.components(g)
vertices <- lapply(bc$components, function(x) unique(as.vector(get.edges(g, x))))
```

*Documentation reproduced from package igraph, version 0.5.3, License: GPL (>= 2)*

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