An articulation vertex of a connected graph, also called a cut-vertex (Harary 1994, p. 26; West 2000; Gross and Yellen 2006) or
"cutpoint" (Harary 1994, p. 26), is a vertex whose removal will disconnect
the graph (Chartrand 1985). More generally, an articulation vertex of a not-necessarily-connected
graph is a vertex whose removal increases the connected
component count (Harary 1994, p. 26; West 2000, p. 23). An example
graph due to West (2000, pp. 22-23) is illustrated above with its articulation
vertices 
and 
indicated.
A graph on two or more vertices possessing no articulation vertices is called a biconnected graph. A vertex is an articulation vertex iff it appears in two biconnected components.
A maximal connected subgraph of a given graph 
that has no articulation vertex is called
a block (West 2000, p. 155).
The endpoints of a graph bridge are articulation vertices unless they both have vertex degree 1. On the other hand, it is possible for a non-bridge edge to have both endpoints be articulation vertices.
The Wolfram Language function FindVertexCut[g]
returns a vertex cut set of smallest size for a
connected graph 
, which corresponds to an articulation vertex if the set is
of size 1.
The analog of an articulation vertex for edges is called a graph bridge.
