GraphDistance
GraphDistance [g,s,t]
gives the distance from source vertex s to target vertex t in the graph g.
GraphDistance [g,s]
gives the distance from s to all vertices of the graph g.
GraphDistance [{vw,…},…]
uses rules vw to specify the graph g.
Details and Options
- GraphDistance is also known as geodesic distance.
- GraphDistance [g,s,t] will give the length of the shortest path between s and t.
- The distance is Infinity when there is no path between s and t.
- For a weighted graph, the distance is the minimum of the sum of weights along any path between s and t.
- The following options can be given:
- Possible Method settings include "Dijkstra", "BellmanFord", and "UnitWeight".
Examples
open allclose allBasic Examples (1)
Give the distance for a grid graph:
Scope (7)
GraphDistance works with undirected graphs:
Directed graphs:
Weighted graphs:
Multigraphs:
Mixed graphs:
Use rules to specify the graph:
GraphDistance works with large graphs:
Options (4)
Method (4)
The method is automatically chosen, depending on input:
"UnitWeight" method will use the weight 1 for every edge:
"Dijkstra" can be used for graphs with positive edge weights only:
"BellmanFord" can be used for directed graphs, including negative edge weights:
Applications (5)
Find the distance between opposite corners of a GridGraph of size {6,6}:
Find the distance between opposite corners in a -dimensional GridGraph of size {6,6,…,6}:
Visualize distance from a vertex in a tree:
Obtain the maximum distance from the vertex to any other vertex:
Set color proportionally to distance:
The expected distance between two vertices for Bernoulli graphs with probability is :
Illustrate the DamerauLevenshteinDistance for short words over a small alphabet:
Find the Damerau–Levenshtein distance between two words:
Check the result:
Properties & Relations (3)
The distance between two vertices can be found using FindShortestPath :
Distance matrix:
In a connected graph, the VertexEccentricity can be computed using GraphDistance :
The distance between two vertices belonging to different connected components is Infinity :
See Also
GraphDistanceMatrix BreadthFirstScan DepthFirstScan
Function Repository: DistanceLayeredGraph
Text
Wolfram Research (2010), GraphDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphDistance.html (updated 2015).
CMS
Wolfram Language. 2010. "GraphDistance." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphDistance.html.
APA
Wolfram Language. (2010). GraphDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphDistance.html
BibTeX
@misc{reference.wolfram_2025_graphdistance, author="Wolfram Research", title="{GraphDistance}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphDistance.html}", note=[Accessed: 22-April-2025 ]}
BibLaTeX
@online{reference.wolfram_2025_graphdistance, organization={Wolfram Research}, title={GraphDistance}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphDistance.html}, note=[Accessed: 22-April-2025 ]}