GraphUtilities`

PseudoDiameter

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

PseudoDiameter[g]

give the pseudo-diameter of the undirected graph g, and the two vertices that achieve this diameter.

Details and Options

PseudoDiameter functionality is now available in the built-in Wolfram Language function GraphDiameter.
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.
If the graph is disconnected, then the diameter and vertices for each connected component are returned.
The following option can be given:
Aggressive False whether to make extra effort in finding the optimal graph diameter