Finding the biconnected components of a graph
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()
Connected components
articulation_points(),
component_distribution(),
decompose(),
is_biconnected()
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(which(clu == 1), which(clu == 2)))
bc <- biconnected_components(g)