Biconnected component

In graph theory, an articulation point, the articulation point of the articulation section or node means a node of a graph the removal of which would increase the number of connected sub-graphs. If the graph was continuous prior to removal of the node, it is then disconnected. A hinge point is a special case of a separator

The term of the articulation point is well defined for directed graphs, but it is mainly used for undirected graphs. Basically can not own more than n- 2 joints a contiguous undirected graph with n nodes.

A bridge is an edge similar to a pivot point; That is, the removal of the bridge increases the number of connected subgraph.

Finding points of articulation

A trivial algorithm:

C = empty set ( after the end of the algorithm it is the articulation points included) a = number of connected subgraph (found with depth-first search / breadth-first search ) for showing all nodes in V i on the edges      b = the number of connected subgraph if i is removed      if b> a          i is an articulation point          C = C { i}      endif endfor There is an algorithm which achieves a much better run time by means of depth-first search.

Pivot points in trees

A node of a tree graph is a pivot point when the degree of the node is greater than 1.