maxweight = extended_numeric

Specifies a maximum weight for the paths returned. Paths exceeding this will be omitted from the iteration. The default is infinity.

output = one of iterator, list, or set

Specifies what is returned from AllSimplePaths. The default is iterator.

AllSimplePaths(G, u, v) returns all simple paths from u to v in a graph G.

The default output is an Iterator.

A simple path is one in which each vertex in the path is distinct.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{C6}≔\mathrm{CycleGraph}\left(6\right)$

$\mathrm{C6}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 6\; edges}$

$\mathrm{IsReachable}\left(\mathrm{C6}\,1\,5\right)$

$\mathrm{true}$

$\mathrm{iter}≔\mathrm{AllSimplePaths}\left(\mathrm{C6}\,1\,5\right)$

$\mathrm{iter}≔\left[\begin{array}{c}\mathrm{Path\; Iterator}\end{array}\right]$

$$\begin{gathered} \mathbf{for}\mathrm{path}\mathbf{in}\mathrm{iter}\mathbf{do} \\ \mathrm{print}\left(\mathrm{path}\right) \\ \mathbf{end}\mathbf{do} \end{gathered}$$

$\left[1\,6\,5\right]$

$\left[1\,2\,3\,4\,5\right]$

$\mathrm{AllSimplePaths}\left(\mathrm{C6}\,1\,5\,\mathrm{output}=\mathrm{set}\right)$

$\left\{\left[1\,6\,5\right]\,\left[1\,2\,3\,4\,5\right]\right\}$

$\mathrm{W6}≔\mathrm{Graph}\left(\left\{\left[\left[1\,2\right]\,10\right]\,\left[\left[1\,6\right]\,6\right]\,\left[\left[2\,3\right]\,-10\right]\,\left[\left[3\,4\right]\,10\right]\,\left[\left[4\,5\right]\,-10\right]\,\left[\left[5\,6\right]\,5\right]\right\}\right)$

$\mathrm{W6}≔\mathrm{Graph\; 2:\; a\; directed\; weighted\; graph\; with\; 6\; vertices\; and\; 6\; arcs}$

$\mathrm{DrawGraph}\left(\mathrm{W6}\,'\mathrm{layout}'='\mathrm{circle}'\right)$

$\mathrm{AllSimplePaths}\left(\mathrm{W6}\,1\,6\,\mathrm{output}=\mathrm{list}\right)$

$\left[\left[1\,6\right]\,\left[1\,2\,3\,4\,5\,6\right]\right]$

$\mathrm{AllSimplePaths}\left(\mathrm{W6}\,6\,1\,\mathrm{output}=\mathrm{list}\right)$

The GraphTheory[AllSimplePaths] command was introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.