Network Action Set

A biconnected component (or block) of a graph is a connected subgraph that you cannot break into disconnected pieces by deleting any single node (and its incident links). An articulation point (or cut point) of a graph is a node whose removal would cause an increase in the number of connected components. Articulation points can be important when you analyze any graph that represents a communications network. Consider an articulation point that, if removed, breaks the graph into two components, and . All paths in G between some nodes in and some nodes in must pass through node i. In this sense, articulation points are critical to communication. Examples where articulation points are important include airline hubs, electric circuits, network wires, protein bonds, traffic routers, and many other industrial applications.

The block-cut tree of a connected graph is an abstract representation of that graph in the form of a tree, where biconnected components, or blocks, are connected through articulation points, or cut points.

For examples of using the biconnectedComponents action, see Finding the Biconnected Components of an Undirected Graph and Finding the Block-Cut Tree of an Undirected Graph.

For more information about biconnected components and the capabilities of the biconnectedComponents action, see the section Biconnected Components and Articulation Points (SAS Viya: NETWORK Procedure).