Ideas for colorfully and clearly highlighting graph edges according to weightsStandardForm on Graph edgesColoring edges of a graph according to their weight?Styling the edges of a graph according to the multiplicities of the edgesChanging edge weights in a graph using PropertyValueCannot get Mathematica to recognise Vertex Weights of GraphOther Ideas for Clickable Graph BuildupHow to style a graph according to the direction of the edges and the centrality of the vertices?FindShortestPath in a Random Geometric Graph: Quick Version?How to filter-out edges in a HighlightGraph[] visualization based on VertexCoordinates[]?Finding the dangling free part of a percolating cluster

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Ideas for colorfully and clearly highlighting graph edges according to weights


StandardForm on Graph edgesColoring edges of a graph according to their weight?Styling the edges of a graph according to the multiplicities of the edgesChanging edge weights in a graph using PropertyValueCannot get Mathematica to recognise Vertex Weights of GraphOther Ideas for Clickable Graph BuildupHow to style a graph according to the direction of the edges and the centrality of the vertices?FindShortestPath in a Random Geometric Graph: Quick Version?How to filter-out edges in a HighlightGraph[] visualization based on VertexCoordinates[]?Finding the dangling free part of a percolating cluster













3












$begingroup$


I am trying to figure out a way to include edgeweights in the visualisation of a graph in Mathematica, to find an idea for the drawing such that even for relatively large node numbers the graphs remain visually clear. But the basic built-in feature leads to rather messy layouts as soon as there are large number of nodes/edges. Here's an example below:



SeedRandom[100]
n = 500;
m = 1000;
edgeweights = 1./RandomReal[0.1, 1, m];
G = RandomGraph[n, m, EdgeWeight -> edgeweights]


Produces:
enter image description here



Including GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True into the definition of G produces:



enter image description here



It seems to simply draw the nodes whose connecting edge weight is larger closer to one another, which leads to a very dense embedded layout.



Would it be possible to:



  • Modulate the edge thickness and color [*] according to their weights? The weights do not necessarily have to be given in the graph definition (G), they could also simply be called for the purpose of the visualisation.

[*]: That is, the greater the weight, the thicker and the more brightly colored the edge. For normalization, we can use the maximal weight in the vector of edgeweights.










share|improve this question









$endgroup$
















    3












    $begingroup$


    I am trying to figure out a way to include edgeweights in the visualisation of a graph in Mathematica, to find an idea for the drawing such that even for relatively large node numbers the graphs remain visually clear. But the basic built-in feature leads to rather messy layouts as soon as there are large number of nodes/edges. Here's an example below:



    SeedRandom[100]
    n = 500;
    m = 1000;
    edgeweights = 1./RandomReal[0.1, 1, m];
    G = RandomGraph[n, m, EdgeWeight -> edgeweights]


    Produces:
    enter image description here



    Including GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True into the definition of G produces:



    enter image description here



    It seems to simply draw the nodes whose connecting edge weight is larger closer to one another, which leads to a very dense embedded layout.



    Would it be possible to:



    • Modulate the edge thickness and color [*] according to their weights? The weights do not necessarily have to be given in the graph definition (G), they could also simply be called for the purpose of the visualisation.

    [*]: That is, the greater the weight, the thicker and the more brightly colored the edge. For normalization, we can use the maximal weight in the vector of edgeweights.










    share|improve this question









    $endgroup$














      3












      3








      3





      $begingroup$


      I am trying to figure out a way to include edgeweights in the visualisation of a graph in Mathematica, to find an idea for the drawing such that even for relatively large node numbers the graphs remain visually clear. But the basic built-in feature leads to rather messy layouts as soon as there are large number of nodes/edges. Here's an example below:



      SeedRandom[100]
      n = 500;
      m = 1000;
      edgeweights = 1./RandomReal[0.1, 1, m];
      G = RandomGraph[n, m, EdgeWeight -> edgeweights]


      Produces:
      enter image description here



      Including GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True into the definition of G produces:



      enter image description here



      It seems to simply draw the nodes whose connecting edge weight is larger closer to one another, which leads to a very dense embedded layout.



      Would it be possible to:



      • Modulate the edge thickness and color [*] according to their weights? The weights do not necessarily have to be given in the graph definition (G), they could also simply be called for the purpose of the visualisation.

      [*]: That is, the greater the weight, the thicker and the more brightly colored the edge. For normalization, we can use the maximal weight in the vector of edgeweights.










      share|improve this question









      $endgroup$




      I am trying to figure out a way to include edgeweights in the visualisation of a graph in Mathematica, to find an idea for the drawing such that even for relatively large node numbers the graphs remain visually clear. But the basic built-in feature leads to rather messy layouts as soon as there are large number of nodes/edges. Here's an example below:



      SeedRandom[100]
      n = 500;
      m = 1000;
      edgeweights = 1./RandomReal[0.1, 1, m];
      G = RandomGraph[n, m, EdgeWeight -> edgeweights]


      Produces:
      enter image description here



      Including GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True into the definition of G produces:



      enter image description here



      It seems to simply draw the nodes whose connecting edge weight is larger closer to one another, which leads to a very dense embedded layout.



      Would it be possible to:



      • Modulate the edge thickness and color [*] according to their weights? The weights do not necessarily have to be given in the graph definition (G), they could also simply be called for the purpose of the visualisation.

      [*]: That is, the greater the weight, the thicker and the more brightly colored the edge. For normalization, we can use the maximal weight in the vector of edgeweights.







      graphics graphs-and-networks visualization






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 6 hours ago









      user929304user929304

      29629




      29629




















          2 Answers
          2






          active

          oldest

          votes


















          2












          $begingroup$

          edgeStyle[weights_, thickbounds_:0.0001,0.01, colorf_:ColorData["SolarColors"]]:=
          Block[minmax, thickness, color,
          minmax = MinMax[weights];
          thickness = Thickness /@ Rescale[weights, minmax, thickbounds];
          color = colorf /@ Rescale[weights, minmax, 0, 1];
          Thread[Directive[Opacity[.7], CapForm["Round"], thickness, color]]
          ]


          Here's the example:



          Graph[G, EdgeStyle -> Thread[EdgeList[G] -> edgeStyle[edgeweights]], 
          VertexSize -> 1, VertexStyle -> Blue]


          enter image description here



          With different thickness and color:



          Graph[G, EdgeStyle -> 
          Thread[EdgeList[G] ->
          edgeStyle[edgeweights, 0.0001, 0.02,
          ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]


          enter image description here






          share|improve this answer









          $endgroup$




















            2












            $begingroup$

            I do not think that any good way exists. Once a graph is large enough, it will always look like a hairball unless it has a clear structure that might be made visible. For example, this is a similarity graph of musicians. The musicians cluster into groups, and it is possible to make this structure visible. Your example graph, on the other hand, is completely random, with random edge weights. Since there are lots of nodes and edges, but no real information is contained within them, I do not think that it can be visualized in a meaningful way.



            Assuming that there is something to show, things you can try are:




            • Take edge weights into consideration when computing the layout. Look up individual graph layouts on the GraphLayout doc page, and see if they support weights. You have already found GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True, but it's still useful to mention this for other readers.



              The example I linked above was created by one of the authors of the igraph library. IGraph/M is a Mathematica interface to igraph (and much more), and exposes multiple layout algorithms that support weights. The above example was created using the DrL layout (IGLayoutDrL function in IGraph/M)




            • Visualize weights as not edge lengths, but edge weights or edge colours. You can do this with EdgeStyle. IGraph/M provides a very convenient way to do it:



              SeedRandom[137]
              g = RandomGraph[10, 20, EdgeWeight -> RandomReal[.1, 1, 20]]

              Graph[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/3]]] //
              IGEdgeMap[AbsoluteThickness[10 #] &, EdgeStyle -> IGEdgeProp[EdgeWeight]]


              enter image description here




            • Use colours in the same way.



              Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
              IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]


              enter image description here




            • Use all of the above: edge length, edge thickness and edge colour.



              IGLayoutFruchtermanReingold[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/2]]] // 
              IGEdgeMap[
              Directive[ColorData["RustTones"][#], AbsoluteThickness[10 #]] &,
              EdgeStyle -> (#/Max[#] &)@*IGEdgeProp[EdgeWeight]]


              enter image description here




            • Cluster the graph vertices before visualizing them. The clustering can take weights into account.



              CommunityGraphPlot[g]


              enter image description here



              This related to what I said above. First, try to identify the structure, then explicitly make it visible.







            share|improve this answer









            $endgroup$













              Your Answer





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              active

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              2












              $begingroup$

              edgeStyle[weights_, thickbounds_:0.0001,0.01, colorf_:ColorData["SolarColors"]]:=
              Block[minmax, thickness, color,
              minmax = MinMax[weights];
              thickness = Thickness /@ Rescale[weights, minmax, thickbounds];
              color = colorf /@ Rescale[weights, minmax, 0, 1];
              Thread[Directive[Opacity[.7], CapForm["Round"], thickness, color]]
              ]


              Here's the example:



              Graph[G, EdgeStyle -> Thread[EdgeList[G] -> edgeStyle[edgeweights]], 
              VertexSize -> 1, VertexStyle -> Blue]


              enter image description here



              With different thickness and color:



              Graph[G, EdgeStyle -> 
              Thread[EdgeList[G] ->
              edgeStyle[edgeweights, 0.0001, 0.02,
              ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]


              enter image description here






              share|improve this answer









              $endgroup$

















                2












                $begingroup$

                edgeStyle[weights_, thickbounds_:0.0001,0.01, colorf_:ColorData["SolarColors"]]:=
                Block[minmax, thickness, color,
                minmax = MinMax[weights];
                thickness = Thickness /@ Rescale[weights, minmax, thickbounds];
                color = colorf /@ Rescale[weights, minmax, 0, 1];
                Thread[Directive[Opacity[.7], CapForm["Round"], thickness, color]]
                ]


                Here's the example:



                Graph[G, EdgeStyle -> Thread[EdgeList[G] -> edgeStyle[edgeweights]], 
                VertexSize -> 1, VertexStyle -> Blue]


                enter image description here



                With different thickness and color:



                Graph[G, EdgeStyle -> 
                Thread[EdgeList[G] ->
                edgeStyle[edgeweights, 0.0001, 0.02,
                ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]


                enter image description here






                share|improve this answer









                $endgroup$















                  2












                  2








                  2





                  $begingroup$

                  edgeStyle[weights_, thickbounds_:0.0001,0.01, colorf_:ColorData["SolarColors"]]:=
                  Block[minmax, thickness, color,
                  minmax = MinMax[weights];
                  thickness = Thickness /@ Rescale[weights, minmax, thickbounds];
                  color = colorf /@ Rescale[weights, minmax, 0, 1];
                  Thread[Directive[Opacity[.7], CapForm["Round"], thickness, color]]
                  ]


                  Here's the example:



                  Graph[G, EdgeStyle -> Thread[EdgeList[G] -> edgeStyle[edgeweights]], 
                  VertexSize -> 1, VertexStyle -> Blue]


                  enter image description here



                  With different thickness and color:



                  Graph[G, EdgeStyle -> 
                  Thread[EdgeList[G] ->
                  edgeStyle[edgeweights, 0.0001, 0.02,
                  ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]


                  enter image description here






                  share|improve this answer









                  $endgroup$



                  edgeStyle[weights_, thickbounds_:0.0001,0.01, colorf_:ColorData["SolarColors"]]:=
                  Block[minmax, thickness, color,
                  minmax = MinMax[weights];
                  thickness = Thickness /@ Rescale[weights, minmax, thickbounds];
                  color = colorf /@ Rescale[weights, minmax, 0, 1];
                  Thread[Directive[Opacity[.7], CapForm["Round"], thickness, color]]
                  ]


                  Here's the example:



                  Graph[G, EdgeStyle -> Thread[EdgeList[G] -> edgeStyle[edgeweights]], 
                  VertexSize -> 1, VertexStyle -> Blue]


                  enter image description here



                  With different thickness and color:



                  Graph[G, EdgeStyle -> 
                  Thread[EdgeList[G] ->
                  edgeStyle[edgeweights, 0.0001, 0.02,
                  ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]


                  enter image description here







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 5 hours ago









                  halmirhalmir

                  10.6k2544




                  10.6k2544





















                      2












                      $begingroup$

                      I do not think that any good way exists. Once a graph is large enough, it will always look like a hairball unless it has a clear structure that might be made visible. For example, this is a similarity graph of musicians. The musicians cluster into groups, and it is possible to make this structure visible. Your example graph, on the other hand, is completely random, with random edge weights. Since there are lots of nodes and edges, but no real information is contained within them, I do not think that it can be visualized in a meaningful way.



                      Assuming that there is something to show, things you can try are:




                      • Take edge weights into consideration when computing the layout. Look up individual graph layouts on the GraphLayout doc page, and see if they support weights. You have already found GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True, but it's still useful to mention this for other readers.



                        The example I linked above was created by one of the authors of the igraph library. IGraph/M is a Mathematica interface to igraph (and much more), and exposes multiple layout algorithms that support weights. The above example was created using the DrL layout (IGLayoutDrL function in IGraph/M)




                      • Visualize weights as not edge lengths, but edge weights or edge colours. You can do this with EdgeStyle. IGraph/M provides a very convenient way to do it:



                        SeedRandom[137]
                        g = RandomGraph[10, 20, EdgeWeight -> RandomReal[.1, 1, 20]]

                        Graph[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/3]]] //
                        IGEdgeMap[AbsoluteThickness[10 #] &, EdgeStyle -> IGEdgeProp[EdgeWeight]]


                        enter image description here




                      • Use colours in the same way.



                        Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
                        IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]


                        enter image description here




                      • Use all of the above: edge length, edge thickness and edge colour.



                        IGLayoutFruchtermanReingold[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/2]]] // 
                        IGEdgeMap[
                        Directive[ColorData["RustTones"][#], AbsoluteThickness[10 #]] &,
                        EdgeStyle -> (#/Max[#] &)@*IGEdgeProp[EdgeWeight]]


                        enter image description here




                      • Cluster the graph vertices before visualizing them. The clustering can take weights into account.



                        CommunityGraphPlot[g]


                        enter image description here



                        This related to what I said above. First, try to identify the structure, then explicitly make it visible.







                      share|improve this answer









                      $endgroup$

















                        2












                        $begingroup$

                        I do not think that any good way exists. Once a graph is large enough, it will always look like a hairball unless it has a clear structure that might be made visible. For example, this is a similarity graph of musicians. The musicians cluster into groups, and it is possible to make this structure visible. Your example graph, on the other hand, is completely random, with random edge weights. Since there are lots of nodes and edges, but no real information is contained within them, I do not think that it can be visualized in a meaningful way.



                        Assuming that there is something to show, things you can try are:




                        • Take edge weights into consideration when computing the layout. Look up individual graph layouts on the GraphLayout doc page, and see if they support weights. You have already found GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True, but it's still useful to mention this for other readers.



                          The example I linked above was created by one of the authors of the igraph library. IGraph/M is a Mathematica interface to igraph (and much more), and exposes multiple layout algorithms that support weights. The above example was created using the DrL layout (IGLayoutDrL function in IGraph/M)




                        • Visualize weights as not edge lengths, but edge weights or edge colours. You can do this with EdgeStyle. IGraph/M provides a very convenient way to do it:



                          SeedRandom[137]
                          g = RandomGraph[10, 20, EdgeWeight -> RandomReal[.1, 1, 20]]

                          Graph[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/3]]] //
                          IGEdgeMap[AbsoluteThickness[10 #] &, EdgeStyle -> IGEdgeProp[EdgeWeight]]


                          enter image description here




                        • Use colours in the same way.



                          Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
                          IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]


                          enter image description here




                        • Use all of the above: edge length, edge thickness and edge colour.



                          IGLayoutFruchtermanReingold[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/2]]] // 
                          IGEdgeMap[
                          Directive[ColorData["RustTones"][#], AbsoluteThickness[10 #]] &,
                          EdgeStyle -> (#/Max[#] &)@*IGEdgeProp[EdgeWeight]]


                          enter image description here




                        • Cluster the graph vertices before visualizing them. The clustering can take weights into account.



                          CommunityGraphPlot[g]


                          enter image description here



                          This related to what I said above. First, try to identify the structure, then explicitly make it visible.







                        share|improve this answer









                        $endgroup$















                          2












                          2








                          2





                          $begingroup$

                          I do not think that any good way exists. Once a graph is large enough, it will always look like a hairball unless it has a clear structure that might be made visible. For example, this is a similarity graph of musicians. The musicians cluster into groups, and it is possible to make this structure visible. Your example graph, on the other hand, is completely random, with random edge weights. Since there are lots of nodes and edges, but no real information is contained within them, I do not think that it can be visualized in a meaningful way.



                          Assuming that there is something to show, things you can try are:




                          • Take edge weights into consideration when computing the layout. Look up individual graph layouts on the GraphLayout doc page, and see if they support weights. You have already found GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True, but it's still useful to mention this for other readers.



                            The example I linked above was created by one of the authors of the igraph library. IGraph/M is a Mathematica interface to igraph (and much more), and exposes multiple layout algorithms that support weights. The above example was created using the DrL layout (IGLayoutDrL function in IGraph/M)




                          • Visualize weights as not edge lengths, but edge weights or edge colours. You can do this with EdgeStyle. IGraph/M provides a very convenient way to do it:



                            SeedRandom[137]
                            g = RandomGraph[10, 20, EdgeWeight -> RandomReal[.1, 1, 20]]

                            Graph[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/3]]] //
                            IGEdgeMap[AbsoluteThickness[10 #] &, EdgeStyle -> IGEdgeProp[EdgeWeight]]


                            enter image description here




                          • Use colours in the same way.



                            Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
                            IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]


                            enter image description here




                          • Use all of the above: edge length, edge thickness and edge colour.



                            IGLayoutFruchtermanReingold[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/2]]] // 
                            IGEdgeMap[
                            Directive[ColorData["RustTones"][#], AbsoluteThickness[10 #]] &,
                            EdgeStyle -> (#/Max[#] &)@*IGEdgeProp[EdgeWeight]]


                            enter image description here




                          • Cluster the graph vertices before visualizing them. The clustering can take weights into account.



                            CommunityGraphPlot[g]


                            enter image description here



                            This related to what I said above. First, try to identify the structure, then explicitly make it visible.







                          share|improve this answer









                          $endgroup$



                          I do not think that any good way exists. Once a graph is large enough, it will always look like a hairball unless it has a clear structure that might be made visible. For example, this is a similarity graph of musicians. The musicians cluster into groups, and it is possible to make this structure visible. Your example graph, on the other hand, is completely random, with random edge weights. Since there are lots of nodes and edges, but no real information is contained within them, I do not think that it can be visualized in a meaningful way.



                          Assuming that there is something to show, things you can try are:




                          • Take edge weights into consideration when computing the layout. Look up individual graph layouts on the GraphLayout doc page, and see if they support weights. You have already found GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True, but it's still useful to mention this for other readers.



                            The example I linked above was created by one of the authors of the igraph library. IGraph/M is a Mathematica interface to igraph (and much more), and exposes multiple layout algorithms that support weights. The above example was created using the DrL layout (IGLayoutDrL function in IGraph/M)




                          • Visualize weights as not edge lengths, but edge weights or edge colours. You can do this with EdgeStyle. IGraph/M provides a very convenient way to do it:



                            SeedRandom[137]
                            g = RandomGraph[10, 20, EdgeWeight -> RandomReal[.1, 1, 20]]

                            Graph[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/3]]] //
                            IGEdgeMap[AbsoluteThickness[10 #] &, EdgeStyle -> IGEdgeProp[EdgeWeight]]


                            enter image description here




                          • Use colours in the same way.



                            Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
                            IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]


                            enter image description here




                          • Use all of the above: edge length, edge thickness and edge colour.



                            IGLayoutFruchtermanReingold[g, EdgeStyle -> Directive[CapForm["Round"], Opacity[1/2]]] // 
                            IGEdgeMap[
                            Directive[ColorData["RustTones"][#], AbsoluteThickness[10 #]] &,
                            EdgeStyle -> (#/Max[#] &)@*IGEdgeProp[EdgeWeight]]


                            enter image description here




                          • Cluster the graph vertices before visualizing them. The clustering can take weights into account.



                            CommunityGraphPlot[g]


                            enter image description here



                            This related to what I said above. First, try to identify the structure, then explicitly make it visible.








                          share|improve this answer












                          share|improve this answer



                          share|improve this answer










                          answered 5 hours ago









                          SzabolcsSzabolcs

                          163k14448945




                          163k14448945



























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