GraphUtilities`
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

# Examples

open allclose all

## Basic Examples(2)

The pseudo-diameter of the graph of a square is 2:

PseudoDiameter has been superseded by GraphDiameter:

## Scope(1)

A graph with disconnected components:

PseudoDiameter returns a list with pseudo-diameters and vertices for each component:

Wolfram Research (2007), PseudoDiameter, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/PseudoDiameter.html.

#### Text

Wolfram Research (2007), PseudoDiameter, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/PseudoDiameter.html.

#### CMS

Wolfram Language. 2007. "PseudoDiameter." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/PseudoDiameter.html.

#### APA

Wolfram Language. (2007). PseudoDiameter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/PseudoDiameter.html

#### BibTeX

@misc{reference.wolfram_2024_pseudodiameter, author="Wolfram Research", title="{PseudoDiameter}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/PseudoDiameter.html}", note=[Accessed: 21-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_pseudodiameter, organization={Wolfram Research}, title={PseudoDiameter}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/PseudoDiameter.html}, note=[Accessed: 21-May-2024 ]}