GraphUtilities`
GraphUtilities`

# GraphPath

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

GraphPath[g,start,end]

finds a shortest path between vertices start and end in graph g.

# Details

• GraphPath functionality is now available in the built-in Wolfram Language function FindShortestPath.
• To use GraphPath, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
• The following options can be used:
•  Method Automatic method to use to find the shortest path Weighted True specify whether edge weight is to be used in calculating distance

# Examples

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## Basic Examples(2)

This defines a small directed graph:

This finds the shortest path from vertex 1 to vertex 3:

This finds the shortest path from vertex 1 to vertex 3, ignoring the edge weights:

GraphPath has been superseded by FindShortestPath:

## Options(1)

### Method(1)

This defines a small graph:

Because of the negative edge weight, the Dijkstra algorithm cannot be applied: The BellmanFord algorithm works:

This defines a small graph with a negative cycle:

The Dijkstra algorithm does not work for negative edge weights: The BellmanFord algorithm detects a negative weight cycle: The default algorithm for graphs with negative edge weights is BellmanFord: ## Properties & Relations(1)

This defines a small directed graph:

This finds the shortest path from vertex 1 to 3:

This finds the distance of this path, taking into account the edge weights:

This finds the distance of this path, ignoring the edge weights:

## Possible Issues(1)

This defines a small directed graph:

If there are negative edge weights, the "Dijkstra" method cannot be used: This finds the shortest path from vertex 1 to vertex 3 using the "BellmanFord" method:

## Interactive Examples(1)

This shows how to travel from vertex 1 to 7 through the shortest path: