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graph theory:)

You probably want to read about biconnected components first; these are just a wrinkle on top of biconnected components.
A *connected component* can be viewed both as an equivalence class of *edges* of a graph **and** as an equivalence class of *vertices* of that graph.A *biconnected component* is an equivalence class of *edges* of a graph. But if we look at the vertices belonging to those edges we don't get an equivalence class; see the diagram at biconnected components for an example.

A vertex belonging to more than one biconnected component is an *articulation point* of the graph. If we remove an articulation point from the graph, it falls apart into several connected components.