GRAPH UTILITIES PACKAGE SYMBOL
PseudoDiameter
PseudoDiameter[g]
give the pseudodiameter of the undirected graph g, and the two vertices that achieve this diameter.
 To use , 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. 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 pseudodiameter.
 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 pseudodiameter of the graph of a square is 2:
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A plot showing the graph, with the two vertices of the pseudodiameter highlighted in red:
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Here is a matrix representation of the graph of a torus:
The pseudodiameter of this torus is 7:
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This finds the graph geodesic between vertices 1 and 26, highlighting the graph geodesic in red:
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