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I have doodled sketches of graphs in JPG format (they roughly look like stick men, in particular the vertices are not shown - they should be where the lines meet) and want to convert them into proper graphs in Mathematica.

Note that I am not concerned about the direction of edges, the graph structure is what matters, not the orientation of the edges or their coordinates; as long as I get a graph that's isomorphic to the sketched graph, that would be fine for me).

What can I do? Any help is welcome! TIA!

This is an example of a sketch that I want Mathematica to turn into a graph

example

When the sketches are a bit more rough with thicker edges, then kglr's (original) approach does not seem to work. I attached another figure. Note that this at first was ONLY the lines with a blank interior. I actually used a paint program to fill the inner part with black, but it did not work accurately, which makes everything more difficult, I guess. Is there anything I can do about this?

example2

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  • $\begingroup$ Graph[{1 \[UndirectedEdge] 2, 3 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 4, 5 \[UndirectedEdge] 4, 4 \[UndirectedEdge] 6, 6 \[UndirectedEdge] 7, 6 \[UndirectedEdge] 8}, PlotTheme -> "IndexLabeled", GraphLayout -> "SpringElectricalEmbedding"] $\endgroup$
    – Bob Hanlon
    Mar 23, 2020 at 17:32

2 Answers 2

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doodle = Import["https://i.stack.imgur.com/QJcLR.jpg"]

enter image description here

mg = MorphologicalGraph @ ColorReplace[doodle, {White -> Black, Black -> White}]

enter image description here

EdgeList[mg]

enter image description here

Graph[mg, PlotTheme -> "VintageDiagram"]

enter image description here

doodle2 = Import["https://i.stack.imgur.com/dRyDA.png"]

enter image description here

mg2 = MorphologicalGraph@
  SkeletonTransform @ Thinning @
    Closing[ColorNegate @ Binarize @ doodle2, DiskMatrix[2]]

enter image description here

Graph[mg2, PlotTheme -> "VintageDiagram"]

enter image description here

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Before using MorphologicalGraph with your image that has thick lines, try thinning, after filling in the noise in your image:

Thinning[FillingTransform[ColorNegate[Binarize[image]]]]

If that leaves a few short edges you don't want, try the Pruning function.

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