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Ideas for colorfully and clearly highlighting graph edges according to weights
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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
$begingroup$
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:
Including GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True
into the definition of G
produces:
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
$endgroup$
add a comment |
$begingroup$
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:
Including GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True
into the definition of G
produces:
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
$endgroup$
add a comment |
$begingroup$
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:
Including GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True
into the definition of G
produces:
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
$endgroup$
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:
Including GraphLayout -> "SpringElectricalEmbedding", "EdgeWeighted" -> True
into the definition of G
produces:
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
graphics graphs-and-networks visualization
asked 6 hours ago
user929304user929304
29629
29629
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
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]
With different thickness and color:
Graph[G, EdgeStyle ->
Thread[EdgeList[G] ->
edgeStyle[edgeweights, 0.0001, 0.02,
ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]
$endgroup$
add a comment |
$begingroup$
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 foundGraphLayout -> "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]]Use colours in the same way.
Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]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]]Cluster the graph vertices before visualizing them. The clustering can take weights into account.
CommunityGraphPlot[g]
This related to what I said above. First, try to identify the structure, then explicitly make it visible.
$endgroup$
add a comment |
Your Answer
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2 Answers
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2 Answers
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$begingroup$
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]
With different thickness and color:
Graph[G, EdgeStyle ->
Thread[EdgeList[G] ->
edgeStyle[edgeweights, 0.0001, 0.02,
ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]
$endgroup$
add a comment |
$begingroup$
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]
With different thickness and color:
Graph[G, EdgeStyle ->
Thread[EdgeList[G] ->
edgeStyle[edgeweights, 0.0001, 0.02,
ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]
$endgroup$
add a comment |
$begingroup$
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]
With different thickness and color:
Graph[G, EdgeStyle ->
Thread[EdgeList[G] ->
edgeStyle[edgeweights, 0.0001, 0.02,
ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]
$endgroup$
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]
With different thickness and color:
Graph[G, EdgeStyle ->
Thread[EdgeList[G] ->
edgeStyle[edgeweights, 0.0001, 0.02,
ColorData["BrightBands"]]], VertexSize -> 1, VertexStyle -> Blue]
answered 5 hours ago
halmirhalmir
10.6k2544
10.6k2544
add a comment |
add a comment |
$begingroup$
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 foundGraphLayout -> "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]]Use colours in the same way.
Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]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]]Cluster the graph vertices before visualizing them. The clustering can take weights into account.
CommunityGraphPlot[g]
This related to what I said above. First, try to identify the structure, then explicitly make it visible.
$endgroup$
add a comment |
$begingroup$
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 foundGraphLayout -> "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]]Use colours in the same way.
Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]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]]Cluster the graph vertices before visualizing them. The clustering can take weights into account.
CommunityGraphPlot[g]
This related to what I said above. First, try to identify the structure, then explicitly make it visible.
$endgroup$
add a comment |
$begingroup$
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 foundGraphLayout -> "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]]Use colours in the same way.
Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]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]]Cluster the graph vertices before visualizing them. The clustering can take weights into account.
CommunityGraphPlot[g]
This related to what I said above. First, try to identify the structure, then explicitly make it visible.
$endgroup$
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 foundGraphLayout -> "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]]Use colours in the same way.
Graph[g, EdgeStyle -> Directive[CapForm["Round"], AbsoluteThickness[4]]] //
IGEdgeMap[ColorData["RustTones"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight]]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]]Cluster the graph vertices before visualizing them. The clustering can take weights into account.
CommunityGraphPlot[g]
This related to what I said above. First, try to identify the structure, then explicitly make it visible.
answered 5 hours ago
SzabolcsSzabolcs
163k14448945
163k14448945
add a comment |
add a comment |
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