Biconnected component

Not to be confused with vertex cut.

Each color corresponds to a biconnected component. Multi-colored vertices are cut vertices, and thus belong to multiple biconnected components.

In graph theory, a biconnected component or block (sometimes known as a 2-connected component) is a maximal biconnected subgraph. Any connected graph decomposes into a tree of biconnected components called the block-cut tree of the graph. The blocks are attached to each other at shared vertices called cut vertices or separating vertices or articulation points. Specifically, a cut vertex is any vertex whose removal increases the number of connected components. A block containing at most one cut vertex is called a leaf block, it corresponds to a leaf vertex in the block-cut tree.