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colorswolfram-mathematicagraph-theoryedges

Creating a graph with edges of different colours in Mathematica

I want to create a graph (Graph Theory) where certain edges have a different colour to other edges, which would be used to highlight a path in the graph from one vertex to another.

Here are some examples which have different coloured edges http://demonstrations.wolfram.com/AGraphTheoryInterpretationOfTheSumOfTheFirstNIntegers/ and http://demonstrations.wolfram.com/Ramsey336/. I looked at source code for these but those solutions seem complicated. I need a simple example to work from. I reckon I need to use the EdgeRenderingFunction as one of the options for GraphPlot.

Additionally under EdgeRenderingFunction documentation in "More Information" part it says:

Mathematica graphics

This looks useful but unfortunately there is no coded examples to try.

Taking that very literally I tried things like

GraphPlot[{1 -> 2, 2 -> 3, 3 -> 4, 4 -> 1, 2 -> 4, 4 -> 5, 4 -> 6}, VertexLabeling -> True,
EdgeRenderingFunction -> g[{1, 2}, {1, 2}, Red]]

But that wouldn't work. It will take something more clever than that.

Solution

  • Here's an example that illustrates how to automate the highlighting of a particular path through a graph.

    Here's a silly graph, specified by a list of edge rules:

    edges = Table[i -> Mod[1 + i^2, 10], {i, 0, 9}];
GraphPlot[edges, VertexLabeling -> True]

    Mathematica graphics

    Here's a path through the graph we'd like to highlight.

    path = {0, 1, 2, 5, 6, 7, 0};

    Let's partition the path into edges, accounting for the fact that we want to highlight the edge independent of its orientation.

    edgesToHighlight = Partition[path, 2, 1];
edgesToHighlight = Join[edgesToHighlight,
    Reverse /@ edgesToHighlight];

    We write an EdgeRenderingFunction that renders an edge in one of two styles, depending no whether it's in our list or not.

    erf[pts_, edge_, ___] := If[MemberQ[edgesToHighlight, edge],
    {Thick, Black, Arrow[pts, 0.1]}, {Darker[Red], Line[pts]}];

    Finally, we display the result.

    GraphPlot[edges, EdgeRenderingFunction -> erf,
    VertexLabeling -> True]

    Mathematica graphics