This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 GRAPH UTILITIES PACKAGE SYMBOL

# PseudoDiameter

 PseudoDiameter[g]give the pseudo-diameter of the undirected graph g, and the two vertices that achieve this diameter.
• 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. 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
The pseudo-diameter of the graph of a square is 2:
A plot showing the graph with the two vertices of the pseudo-diameter highlighted in red:
Here is a matrix representation of the graph of a torus:
The pseudo-diameter of this torus is 7:
This finds the graph geodesic between vertices 1 and 26, highlighting the graph geodesic in red:
Needs["GraphUtilities`"]
The pseudo-diameter of the graph of a square is 2:
 Out[3]=
A plot showing the graph with the two vertices of the pseudo-diameter highlighted in red:
 Out[4]=

Needs["GraphUtilities`"]
Here is a matrix representation of the graph of a torus:
The pseudo-diameter of this torus is 7:
 Out[3]=
This finds the graph geodesic between vertices 1 and 26, highlighting the graph geodesic in red:
 Out[5]=
 Scope   (1)
A graph with disconnected components:
returns a list with pseudo-diameters and vertices for each component:
This shows a small directed graph:
This finds the pseudo-diameter of the directed graph:
GraphDistance and GraphPath find that there is no path from 4 to 1 in the directed graph:
This turns into an undirected graph:
GraphDistance and GraphPath now find a path of length 2: