# FindPath

FindPath[g,s,t]

finds a path between vertex s and vertex t in the graph g.

FindPath[g,s,t,k]

finds a path of length at most k between vertex s and vertex t in the graph g.

FindPath[g,s,t,{k}]

finds a path of length exactly k.

FindPath[g,s,t,{kmin,kmax}]

finds a path of length between kmin and kmax.

FindPath[g,s,t,kspec,n]

finds at most n paths.

FindPath[{vw,},]

uses rules vw to specify the graph g.

# Details • FindPath returns a list of paths from s to t. Each path is given as a list of vertices.
• FindPath[g,s,t,kspec,All] finds all the paths.
• For weighted graphs, FindPath[g,s,t,k] gives all paths with total weights at most k.
• FindPath works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(2)

Find a path between two individual vertices in a graph:

Highlight the path:

Find all paths between two individual vertices in a graph:

## Scope(12)

### Specification(7)

FindPath works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Weighted graphs:

Use rules to specify the graph:

FindPath works with large graphs:

### Enumeration(5)

A path of length exactly 7:

A path of length at most 6:

A path of length between 5 and 7:

Find all paths between two individual vertices:

FindPath gives an empty list if there is no path:

## Applications(2)

Find paths of length at most 5 along the seams of a soccer ball:

Highlight the paths:

Plan a trip in the London Underground:

Find a trip from Arsenal to Alperton with at most 16 stops:

## Properties & Relations(2)

Find all shortest paths:

Highlight results:

FindPath only returns simple paths: