Finding the biconnected components of a graph
- The input graph. It is treated as an undirected graph, even if it is directed.
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.
- 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
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)