igraph (version 1.0.0)

biconnected_components: 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.

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.

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.

See Also

articulation_points, components, is_connected, vertex_connectivity

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)

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