BUILT-IN MATHEMATICA SYMBOL

GraphDistance

gives the distance from source vertex s to target vertex t in the graph g.

gives the distance from s to all vertices of the graph g.

For a weighted graph, the distance is the minimum of the sum of weights along any path between s and t.

Give the distance for a grid graph:

Out[1]=

Out[2]=

GraphDistance works with undirected graphs:

Directed graphs:

Weighted graphs:

The distance between two vertices is the smallest total edge weight along any path:

Works with large graphs:

The method is automatically chosen depending on input:

method will use the weight 1 for every edge:

can be used for graphs with positive edge weights only:

Find the distance between opposite corners of a GridGraph of size

:

Find the distance between opposite corners in a

-dimensional GridGraph of size

:

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:

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: