A biconnected component is a maximal connected subgraph with no cut vertex of its own. We use the block convention that also includes each bridge in a graph with its two endpoint vertices, and each isolated vertex, as a biconnected component. A biconnected component with at least three vertices stays connected after any single vertex deletion. Distinct biconnected components share at most one vertex; the vertices belonging to more than one biconnected component are exactly the cut vertices. The shared- example has two biconnected components, its two triangles in a graph. The joined- example has three: , the bridge in a graph with its endpoints, and . The edges partition into these pieces, while the shared cut vertices occur in several pieces. [ref]
https://algs4.cs.princeton.edu/41graph/. Sedgewick and Wayne, Algorithms, §4.1, biconnected components exercises
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A **biconnected component** (also known as a biconnected subgraph) is a concept from graph theory that refers to a maximal subgraph in which any two vertices are connected to each other by two disjoint paths. In simpler terms, a biconnected component is a section of a graph where the removal of any single vertex (and the edges incident to it) will not disconnect the component.