The PathWeight(G) command returns the path weight of the walk w in the graph G.

When G is weighted, this is the sum of the edge weights for all edges appearing in the walk w.

When G is unweighted, this is simply the number of edges of the walk.

Note that self-loops appearing in w are not included in the edge count for the purposes of computing graph density.

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

$\mathrm{K4}≔\mathrm{CompleteGraph}\left(4\right)$

$\mathrm{K4}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 6\; edge(s)}$

$\mathrm{PathWeight}\left(\mathrm{K4}\,\left[1\,2\,3\,4\right]\right)$

$4$

$\mathrm{GS}≔\mathrm{Graph}\left(3\,\mathrm{Matrix}\left(3\,\left[\left[0\,2\,3\right]\,\left[2\,0\,4\right]\,\left[5\,3\,3\right]\right]\right)\right)$

$\mathrm{GS}≔\mathrm{Graph\; 2:\; a\; directed\; weighted\; graph\; with\; 3\; vertices,\; 6\; arc(s),\; and\; 1\; self-loop(s)}$

$\mathrm{PathWeight}\left(\mathrm{GS}\,\mathrm{Trail}\left(1\,2\,3\,3\,1\right)\right)$

$14$

$\mathrm{BavarianCities}≔\mathrm{Import}\left(''example/bayern10.csv''\,\mathrm{base}=\mathrm{datadir}\,\mathrm{output}=\mathrm{Matrix}\right)$

$\mathrm{BavarianCities}≔\left[\begin{array}{ccc}''München''& 48.137222& 11.575556\\ ''Nürnberg''& 49.455556& 11.078611\\ ''Augsburg''& 48.371667& 10.898333\\ ''Regensburg''& 49.017222& 12.096944\\ ''Ingolstadt''& 48.76415& 11.42434\\ ''Würzburg''& 49.79441& 9.92937\\ ''Fürth''& 49.4774& 10.98844\\ ''Erlangen''& 49.596361& 11.004311\\ ''Bamberg''& 49.891667& 10.891667\\ ''Bayreuth''& 49.9475& 11.5775\end{array}\right]$

$\mathrm{G1}≔\mathrm{GraphTheory}:-\mathrm{CompleteGraph}\left(\mathrm{convert}\left(\mathrm{BavarianCities}\left[..,1\right]\,\mathrm{list}\right)\,\mathrm{vertexpositions}=\mathrm{BavarianCities}\left[..,2..3\right]\right)$

$\mathrm{G1}≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 45\; edge(s)}$

$\mathrm{G2}≔\mathrm{MakeWeighted}\left(\mathrm{G1}\,\mathrm{vertexpositions}\,\mathrm{metric}=\mathrm{Euclidean}\right)$

$\mathrm{G2}≔\mathrm{Graph\; 4:\; an\; undirected\; weighted\; graph\; with\; 10\; vertices\; and\; 45\; edge(s)}$

$\mathrm{PathWeight}\left(\mathrm{G2}\,\left[''M303274nchen''\,''Regensburg''\,''Bayreuth''\,''Bamberg''\,''Erlangen''\,''W303274rzburg''\,''F303274rth''\,''N303274rnberg''\,''Ingolstadt''\,''Augsburg''\,''M303274nchen''\right]\right)$

$7.52978991560743$

The GraphTheory[PathWeight] command was introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.