Graph Utilities Package Symbol

PseudoDiameter

PseudoDiameter[g]
gives the pseudo diameter of the undirected graph g, and the two vertices that achieve this diameter.

To use PseudoDiameter, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].

A graph geodesic is a shortest path between two vertices of a graph. The graph diameter is the longest possible length of all graph geodesics of the graph. PseudoDiameter finds an approximate graph diameter. It works by starting from a vertex u, and finds a vertex v that is farthest away from u. This process is repeated by treating v as the new starting vertex, and ends when the graph distance no longer increases. A vertex from the last level set that has the smallest degree is chosen as the final starting vertex u, and a traversal is done to see if the graph distance can be increased. This graph distance is taken to be the pseudo diameter.