Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Weighted
SimpleGraph with edge and vertex weights
Contributed by:
Nikolay Murzin
ResourceFunction["WeightedSimpleGraph"][g] gives the underlying simple graph from the graph g with edge weights corresponding to edge multiplicities. | |
ResourceFunction["WeightedSimpleGraph"][g,f] also applies function f to vertices of the graph g and assigns vertex weights based on produced tally. |
Details and Options
ResourceFunction["WeightedSimpleGraph"][g] removes all self-loops and multiple edges between the same vertices.
Self-loops can also be weighted by including SelfLoops→True option.
ResourceFunction["WeightedSimpleGraph"] works with undirected graphs, directed graphs, multigraphs, and mixed graphs.
Examples
Basic Examples (3)
Remove multi-edges from a graph and assign edge weights with their multiplicities:
| In[1]:= | ![ResourceFunction["WeightedSimpleGraph"][\!\(\*
GraphicsBox[
NamespaceBox["NetworkGraphics",
DynamicModuleBox[{Typeset`graph = HoldComplete[
Graph[{1, 2, 3}, {{{1, 2}, {1, 2}, {2, 3}, {2, 3}, {2, 3}}, Null}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData["
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"], {
{Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[
BezierCurveBox[{1, {0.4999999999999994, 0.16444074718311658`}, 2}], 0.02261146496815286], ArrowBox[
BezierCurveBox[{1, {
0.4999999999999998, -0.1644407471831159}, 2}], 0.02261146496815286], ArrowBox[
BezierCurveBox[{2, {1.499999999999998, 0.16444074718311621`}, 3}], 0.02261146496815286], ArrowBox[{2, 3}, 0.02261146496815286], ArrowBox[
BezierCurveBox[{2, {
1.4999999999999984`, -0.1644407471831161}, 3}], 0.02261146496815286]},
{Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.02261146496815286], DiskBox[2, 0.02261146496815286], DiskBox[3, 0.02261146496815286]}}]],
MouseAppearanceTag["NetworkGraphics"]],
AllowKernelInitialization->False]],
DefaultBaseStyle->{"NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]},
FormatType->TraditionalForm,
FrameTicks->None,
ImageSize->{246.73828125, Automatic}]\), EdgeLabels -> "EdgeWeight"]](https://www.wolframcloud.com/obj/resourcesystem/images/0bf/0bfcf2d1-0301-4de4-9e83-c2b65faceb3f/1eaa45bdcaf531e5.png) |
| Out[1]= |  |
Work with mixed graphs:
| In[2]:= | ![ResourceFunction[
"WeightedSimpleGraph"][{1 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 1,
2 \[DirectedEdge] 3, 2 \[DirectedEdge] 3, 3 -> 1}, EdgeLabels -> "EdgeWeight"]](https://www.wolframcloud.com/obj/resourcesystem/images/0bf/0bfcf2d1-0301-4de4-9e83-c2b65faceb3f/11f9098a68df058e.png){kind=small} |
| Out[2]= |  |
Merge each vertex using a function and assign vertex weight based on the number of original vertices producing the same result:
| In[3]:= | ![ResourceFunction["WeightedSimpleGraph"][\!\(\*
GraphicsBox[
NamespaceBox["NetworkGraphics",
DynamicModuleBox[{Typeset`graph = HoldComplete[
Graph[{1, 12, 22, 3}, {{{1, 2}, {1, 3}, {2, 4}, {1, 4}}, Null}, {VertexLabels -> {
Placed[Automatic, Below]}, VertexLabelStyle -> {Bold}, VertexSize -> {0.1}, VertexStyle -> {22 -> RGBColor[1, 0, 0], 12 -> RGBColor[1, 0, 0]}}]]},
TagBox[GraphicsGroupBox[{
{Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[{{0., 2.}, {-1., 1.}}, 0.05], ArrowBox[{{0., 2.}, {0., 1.}}, 0.05], ArrowBox[BezierCurveBox[CompressedData["
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"]], 0.05], ArrowBox[{{-1., 1.}, {1., 0.}}, 0.05]},
{Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[
0.7]}], {DiskBox[{0., 2.}, 0.05], InsetBox[
StyleBox["1",
StripOnInput->False,
FontWeight->Bold], Offset[{0, -2}, {0., 1.95}], ImageScaled[{0.5, 1}],
BaseStyle->"Graphics"]}, {
{RGBColor[1, 0, 0], DiskBox[{-1., 1.}, 0.05]}, InsetBox[
StyleBox["12",
StripOnInput->False,
FontWeight->Bold], Offset[{0, -2}, {-1., 0.95}], ImageScaled[{0.5, 1}],
BaseStyle->"Graphics"]}, {
{RGBColor[1, 0, 0], DiskBox[{0., 1.}, 0.05]}, InsetBox[
StyleBox["22",
StripOnInput->False,
FontWeight->Bold], Offset[{0, -2}, {0., 0.95}], ImageScaled[{0.5, 1}],
BaseStyle->"Graphics"]}, {DiskBox[{1., 0.}, 0.05], InsetBox[
StyleBox["3",
StripOnInput->False,
FontWeight->Bold], Offset[{0, -2}, {1., -0.05}], ImageScaled[{0.5, 1}],
BaseStyle->"Graphics"]}}}],
MouseAppearanceTag["NetworkGraphics"]],
AllowKernelInitialization->False]],
DefaultBaseStyle->{"NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]},
FormatType->TraditionalForm,
FrameTicks->None]\), Mod[#, 10] &, VertexLabels -> "VertexWeight"]](https://www.wolframcloud.com/obj/resourcesystem/images/0bf/0bfcf2d1-0301-4de4-9e83-c2b65faceb3f/18971b03ab8e8cff.png) |
| Out[3]= |  |
Options (1)
SelfLoops (1)
Self-loops can also be weighted:
| In[4]:= | ![ResourceFunction["WeightedSimpleGraph"][\!\(\*
GraphicsBox[
NamespaceBox["NetworkGraphics",
DynamicModuleBox[{Typeset`graph = HoldComplete[
Graph[{1, 2}, {{{1, 2}, {1, 2}}, {{1, 1}, {1, 1}, {1, 1}}}]]},
TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData["
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"], {
{Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium],
{Arrowheads[0.], ArrowBox[BezierCurveBox[{1, 6, 9, 11, 17, 19, 22, 1},
SplineDegree->7], 0.01273]},
{Arrowheads[0.], ArrowBox[BezierCurveBox[{1, 29, 32, 34, 40, 42, 45, 1},
SplineDegree->7], 0.01273]},
{Arrowheads[0.], ArrowBox[BezierCurveBox[{1, 52, 55, 57, 63, 65, 68, 1},
SplineDegree->7], 0.01273]}, ArrowBox[
BezierCurveBox[{1, {
0.5000000000000006, -0.16444074718311627`}, 2}], 0.01273], ArrowBox[
BezierCurveBox[{1, {0.5000000000000001, 0.16444074718311646`}, 2}], 0.01273]},
{Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.01273], DiskBox[2, 0.01273]}}]],
MouseAppearanceTag["NetworkGraphics"]],
AllowKernelInitialization->False]],
DefaultBaseStyle->{"NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]},
FormatType->TraditionalForm,
FrameTicks->None,
ImageSize->{183.34375, Automatic}]\), SelfLoops -> True, EdgeLabels -> "EdgeWeight"]](https://www.wolframcloud.com/obj/resourcesystem/images/0bf/0bfcf2d1-0301-4de4-9e83-c2b65faceb3f/26f1e4bb0990ad42.png) |
| Out[4]= |  |
Applications (1)
Produce weighted evolution graph from its full evolution graph for the MultiwaySystem:
| In[5]:= | ![ResourceFunction["WeightedSimpleGraph"][
ResourceFunction["MultiwaySystem"][{"A" -> "ABA", "AA" -> "B"}, "AABAA", 2, "EvolutionGraphFullStructure"], EdgeLabels -> "EdgeWeight", AspectRatio -> 1/3]](https://www.wolframcloud.com/obj/resourcesystem/images/0bf/0bfcf2d1-0301-4de4-9e83-c2b65faceb3f/403bbf8a91b4db51.png) |
| Out[5]= |  |
| In[6]:= | ![ResourceFunction["MultiwaySystem"][{"A" -> "ABA", "AA" -> "B"}, "AABAA", 2, "EvolutionGraphWeightedStructure", EdgeLabels -> "EdgeWeight"]](https://www.wolframcloud.com/obj/resourcesystem/images/0bf/0bfcf2d1-0301-4de4-9e83-c2b65faceb3f/463f3b29883663c5.png){kind=small} |
| Out[6]= |  |
Properties and Relations (1)
Edge weights assigned by WeightedSimpleGraph can also be computed with EdgeMultiplicity:
| In[7]:= | ![ResourceFunction["EdgeMultiplicity"][\!\(\*
GraphicsBox[
NamespaceBox["NetworkGraphics",
DynamicModuleBox[{Typeset`graph = HoldComplete[
Graph[{1, 2}, {{{1, 2}, {1, 2}}, {{1, 1}, {1, 1}, {1, 1}}}]]},
TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData["
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"], {
{Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium],
{Arrowheads[0.], ArrowBox[BezierCurveBox[{1, 6, 9, 11, 17, 19, 22, 1},
SplineDegree->7], 0.01273]},
{Arrowheads[0.], ArrowBox[BezierCurveBox[{1, 29, 32, 34, 40, 42, 45, 1},
SplineDegree->7], 0.01273]},
{Arrowheads[0.], ArrowBox[BezierCurveBox[{1, 52, 55, 57, 63, 65, 68, 1},
SplineDegree->7], 0.01273]}, ArrowBox[
BezierCurveBox[{1, {
0.5000000000000006, -0.16444074718311627`}, 2}], 0.01273], ArrowBox[
BezierCurveBox[{1, {0.5000000000000001, 0.16444074718311646`}, 2}], 0.01273]},
{Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.01273], DiskBox[2, 0.01273]}}]],
MouseAppearanceTag["NetworkGraphics"]],
AllowKernelInitialization->False]],
DefaultBaseStyle->{"NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]},
FormatType->TraditionalForm,
FrameTicks->None,
ImageSize->{183.34375, Automatic}]\)]](https://www.wolframcloud.com/obj/resourcesystem/images/0bf/0bfcf2d1-0301-4de4-9e83-c2b65faceb3f/750a29a7c2b7d11c.png) |
| Out[7]= |  |
Version History
- 1.1.0 – 03 February 2023
- 1.0.0 – 24 October 2022
Related Resources
Related Symbols
License Information
This work is licensed under a Creative Commons Attribution 4.0 International License