colorscheme : colors

This sets edgecolor using ColorTools:-Blend

thicknessscheme: nonnegative

This sets edgethickness. The value can be zero, but for best results should be positive

arrowsizescheme : nonnegative

This sets arrowsize

arrowposscheme : 0..1

This sets arrowpos

arrowshapescheme : string

This sets arrowshape. Only valuesplit schemes are supported.

linestylescheme : string

This sets linestyle. Only valuesplit schemes are supported.

scheme : list_of_styles

This only supports valuesplit schemes.  For each value a custom list of stylesheet properties can be given.

range=range(numeric)

All styling schemes scale the values in P to the range $0..1$ based on the minimum and maximum values in P.  The range option overrides that and does a linear scaling where lhs(range) becomes to 0 and rhs(range) becomes 1.  This is useful for achieving consistent styling across multiple graphs.  After scaling, values less than 0 will be treated the same as 0 and values greater than 1 will be treated the same as 1.

markers=list(numeric)

By default all the styling schemes linearly interpolate between styles equally spaced across on interval. The markers option allows you to specify exactly which values between 0 and 1 are assigned to each style.  The value of markers must be a sorted list of values between 0 and 1 which is the same length as the list of values given to each scheme.

Limitation: If multiple style schemes are being used with markers all the schemes must have the same number of values. The best work around is to just invoke this command twice on the same graph.

By default the DrawGraph command draws the edges and vertices of the graph with the same set of style options. The command StyleEdgesByProperty, allows you to set styles for all vertices according to a property.

Every style scheme can also be given as a valuesplit scheme. Instead of a list of values to blend between, a valuesplit scheme assigns a discrete set of styles by exact value, range, or list or set of values given as a list of equations and default value. The equations match the property value to the left-hand side and use the value on the right-hand side. For example, colorscheme=["valuesplit", [1="Blue", 2..3="Red", [4,5]="Green", "DarkGrey"] ] If no default value is given, unmatched properties will not be given a style.

By default, this command modifies G and returns nothing. If you supply the option inplace = false, then instead the changes are applied to a copy of G, and that copy is returned.

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

$G≔\mathrm{Graph}\left(\mathrm{weighted}\,\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{2\,3\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\,\left\{4\,6\right\}\,\left\{5\,6\right\}\right\}\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; weighted\; graph\; with\; 6\; vertices\; and\; 7\; edge(s)}$

$\mathrm{RandomGraphs}:-\mathrm{AssignEdgeWeights}\left(G\,1..10\right)$

$\mathrm{Graph\; 1:\; an\; undirected\; weighted\; graph\; with\; 6\; vertices\; and\; 7\; edge(s)}$

$\mathrm{StyleEdgesByProperty}\left(G\,\mathrm{WeightMatrix}\,\mathrm{colorscheme}=\left[''Blue''\,''Red''\right]\,\mathrm{thicknessscheme}=\left[0.5\,2.5\right]\right)$

$\mathrm{DrawGraph}\left(G\right)$

$\mathrm{G2}≔\mathrm{SpecialGraphs}:-\mathrm{PetersenGraph}\left(\right)$

$\mathrm{G2}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$c≔\mathrm{EdgeChromaticNumber}\left(\mathrm{G2}\,'\mathrm{coloring}'\right)$

$c≔4$

edgecolor := proc(G) local i, e, color;
for e in Edges(G) do
   for i from 1 to nops(coloring) do
       if e in coloring[i] then
           color[e[]] := i;
       end if;
   end do;
 end do;
return color;
end proc;

$\mathrm{edgecolor}≔\mathbf{proc}\left(G\right)\mathbf{local}i\,e\,\mathrm{color}\;\mathbf{for}e\mathbf{in}\mathrm{GraphTheory}:-\mathrm{Edges}\left(G\right)\mathbf{do}\mathbf{for}i\mathbf{to}\mathrm{nops}\left(\mathrm{coloring}\right)\mathbf{do}\mathbf{if}e\mathbf{in}\mathrm{coloring}\[i\]\mathbf{then}\mathrm{color}\[e\[\]\]≔i\mathbf{end\; if}\mathbf{end\; do}\mathbf{end\; do}\;\mathbf{return}\mathrm{color}\mathbf{end\; proc}$

$\mathrm{G3}≔\mathrm{StyleEdgesByProperty}\left(\mathrm{G2}\,\mathrm{edgecolor}\,\mathrm{colorscheme}=\left[''valuesplit''\,\left[\mathrm{seq}\left(i=\mathrm{cat}\left(''Bright''\,i\right)\,i=1..c\right)\right]\right]\,\mathrm{inplace}=\mathrm{false}\right)$

$\mathrm{G3}≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{DrawGraph}\left(\mathrm{G3}\right)$

$\mathrm{StyleEdgesByProperty}\left(\mathrm{G2}\,\mathrm{edgecolor}\,\mathrm{linestylescheme}=\left[''valuesplit''\,\left[1=''solid''\,2=''dash''\,3=''dot''\,4=''dashdot''\right]\right]\right)$

$\mathrm{DrawGraph}\left(\mathrm{G2}\right)$

The GraphTheory[StyleEdgesByProperty] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.