# biconnected_components

0th

Percentile

##### 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.

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.

articulation_points, components, is_connected, vertex_connectivity

##### Aliases
• biconnected_components
• biconnected.components
##### Examples
# NOT RUN {
g <- disjoint_union( make_full_graph(5), make_full_graph(5) )
clu <- components(g)\$membership