WOLFRAM

Wolfram Language & System Documentation Center

PseudoDiameter[g]

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

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
See Also
Tech Notes
Related Guides
Cite this Page
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:
  • AggressiveFalsewhether to make extra effort in finding the optimal graph diameter

Examples

open all close all

Basic Examples  (2)

Wolfram Language code: Needs["GraphUtilities`"]

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

Wolfram Language code: g = {1 -> 2, 2 -> 3, 3 -> 4, 4 -> 1};
Wolfram Language code: PseudoDiameter[g]

PseudoDiameter has been superseded by GraphDiameter:

Wolfram Language code: g = Graph[{12, 23, 34, 41}];
Wolfram Language code: {GraphDiameter[g, Method -> "PseudoDiameter"], GraphPeriphery[g, Method -> "PseudoDiameter"]}

Scope  (1)

Wolfram Language code: Needs["GraphUtilities`"]

A graph with disconnected components:

Wolfram Language code: g = {1 -> 2, 2 -> 3, 4 -> 5}

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

Wolfram Language code: PseudoDiameter[g]
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_2026_pseudodiameter, author="Wolfram Research", title="{PseudoDiameter}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/PseudoDiameter.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_pseudodiameter, organization={Wolfram Research}, title={PseudoDiameter}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/PseudoDiameter.html}, note=[Accessed: 13-June-2026]}