biconnected_components: Biconnected components

In igraph: Network Analysis and Visualization

Biconnected components

Description

Finding the biconnected components of a graph

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().

Related documentation in the C library

igraph_biconnected_components().

Author(s)

Gabor Csardi [e-mail]

See Also

articulation_points(), components(), is_connected(), vertex_connectivity()

Connected components articulation_points(), component_distribution(), decompose(), is_biconnected()

Examples

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)

igraph documentation built on Oct. 20, 2024, 1:06 a.m.