`articulation_points()`

finds the articulation points (or cut vertices)

## Value

For `articulation_points()`

, a numeric vector giving the vertex
IDs of the articulation points of the input graph. For `bridges()`

, a
numeric vector giving the edge IDs of the bridges of the input graph.

## Details

Articulation points or cut vertices are vertices whose removal increases the number of connected components in a graph. Similarly, bridges or cut-edges are edges whose removal increases the number of connected components in a graph. If the original graph was connected, then the removal of a single articulation point or a single bridge makes it undirected. If a graph contains no articulation points, then its vertex connectivity is at least two.

## See also

`biconnected_components()`

, `components()`

,
`is_connected()`

, `vertex_connectivity()`

,
`edge_connectivity()`

Connected components
`biconnected_components()`

,
`component_distribution()`

,
`decompose()`

Connected components
`biconnected_components()`

,
`component_distribution()`

,
`decompose()`

## 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(match(1, clu), match(2, clu)))
articulation_points(g)
#> + 2/10 vertices, from 4d43c90:
#> [1] 6 1
g <- make_graph("krackhardt_kite")
bridges(g)
#> + 2/18 edges from 471e9ed:
#> [1] 9--10 8-- 9
```