Articulation points and bridges of a graph

articulation_points() finds the articulation points (or cut vertices)

Usage

articulation_points(graph)

bridges(graph)

Arguments

graph

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

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 disconnected. 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(), is_biconnected()

Author

Gabor Csardi csardi.gabor@gmail.com

Related documentation in the C library

igraph_articulation_points(), igraph_bridges().

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 1d05005:
#> [1] 6 1

g <- make_graph("krackhardt_kite")
bridges(g)
#> + 2/18 edges from b4ab83a:
#> [1] 9--10 8-- 9