Biconnected component

<p>In <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, a biconnected component or block (sometimes known as a 2-connected component) is a maximal <a href="/facts/Biconnected_graph/sTfSnFkM">biconnected</a> <a href="/facts/Glossary_of_graph_theory/W0MqKkyE">subgraph</a>.  Any <a href="/facts/Connectivity_(graph_theory)/FSNjsYhz">connected graph</a> decomposes into a <a href="/facts/Tree_(graph_theory)/TCWk4Joy">tree</a> of biconnected components called the block-cut tree of the graph. The blocks are attached to each other at shared <a href="/facts/Vertex_(graph_theory)/WhlWmL3o">vertices</a> called cut vertices or separating vertices or articulation points.  Specifically, a cut vertex is any vertex whose removal increases the number of <a href="/facts/Connected_component_(graph_theory)/5owVSXtY">connected components</a>. A block containing at most one cut vertex is called a leaf block, it corresponds to a <a href="/facts/Vertex_(graph_theory)/WhlWmL3o">leaf vertex</a> in the block-cut tree.
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Biconnected component open-in-new

Biconnected component