A biconnected component of a graph is a maximally biconnected
subgraph. A graph is biconnected if it does not contain any cut vertices.

Decomposing a graph into its biconnected components helps to measure how
well-connected the graph is. You can decompose any connected graph into a tree of
biconnected components, called the *block-cut tree*. The blocks
in the tree are attached at shared vertices, which are the cut vertices.

The illustration depicts:

(a) An undirected graph with 11 nodes.

(b) Five biconnected components of the graph, with the cut vertices of the
original graph colored for each component to which they belong.

(c) Block-cut tree of the graph, which contains a node for each
biconnected component (as large circles) and a node for each cut vertex (as
smaller multicolored circles). In the block-cut tree, an edge connects each
cut vertex to each component to which it belongs.