In graph theory, a biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain connected.

Jul 23, 2025 · An undirected graph is called Biconnected if there are two vertex-disjoint paths between any two vertices. In a Biconnected Graph, there is a simple cycle through any two vertices.

Dec 3, 2025 · Biconnected graphs are closely related to blocks. If a block has more than two vertices, then it is biconnected (West 2000, p. 155). Conversely, biconnected graphs on two or more vertices …

Sep 22, 2020 · A biconnected graph is a connected graph that has no articulation points. A biconnected component (BCC) (or block) of a connected undirected graph is a maximal biconnected subgraph.

May 27, 2025 · Learn about biconnected graphs, their properties, and significance in graph theory, along with real-world applications and examples.

Edge: Every edge belongs to exactly one biconnected component. Articulation Points: A node can have multiple biconnected components, but it can be an articulation point for only one of them.

Biconnected graph: A graph with no articulation point called biconnected. In other words, a graph is biconnected if and only if any vertex is deleted, the graph remains connected.

Dec 17, 2004 · Definition: A connected graph that is not broken into disconnected pieces by deleting any single vertex (and incident edges). See alsocut vertex, biconnected component, triconnected graph, …

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 …

Now what to look for in a graph to check if it's Biconnected. By now it is said that a graph is Biconnected if it has no vertex such that its removal increases the number of connected components in the graph.