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. components The components themselves, a list of numeric vectors. Each vector is a set of edge ids giving the edges in a biconnected component. articulation_points The articulation points of the graph. See
- See examples below on how to extract the vertex ids of the biconnected components from the result.
g <- graph.disjoint.union( graph.full(5), graph.full(5) ) clu <- clusters(g)$membership g <- add.edges(g, c(which(clu==0), which(clu==1))-1) bc <- biconnected.components(g) vertices <- lapply(bc$components, function(x) unique(as.vector(get.edges(g, x))))