New answers tagged graphs-and-networks
2
To see geng's options, just rung geng -h on the command line.
You can use something like this to e.g. generate connected graphs (-c) on 5 vertices (5) with 6 to 7 edges (6:7):
geng = StartProcess[{"/opt/local/bin/geng", "-c", "5" , "6:7"}]
This does generate all graphs without stopping. But we can read them into Mathematica one by one instead of reading ...
1
The nauty tool includes the program geng which can generate all non-isomorphic graphs with various constraints (including on the number of vertices, edges, connectivity, biconnectivity, triangle-free and others). Its output is in the Graph6 format, which Mathematica can import.
For example, assuming you have geng installed in /opt/local/bin,
Import["!/opt/...
2
(This answer is basically the same as @kglr's, but avoids post-processing and includes a discovery mechanism.)
You can use the "Options" discovery mechanism to find out the options supported by a particular graph element:
GraphElementData["ShortFilledArrow", "Options"]
{"ArrowSize" -> Automatic, "ArrowPositions" -> Automatic}
Your desired Arrowheads ...
2
LayeredGraphPlot[edges, Left,
EdgeShapeFunction -> ({Black, If[MemberQ[{"vertex5"}, Last@#2], Line@#,
GraphElementData[{"ShortFilledArrow"}][##]]} &)]
To change the size and/or position of the arrow glyph you can use:
LayeredGraphPlot[edges, Left,
EdgeShapeFunction -> ({Black, If[MemberQ[{"vertex5"}, Last@#2], Line@#,
...
5
communities = GatherBy[VertexList[g], PropertyValue[{g, #}, VertexStyle] &];
CommunityGraphPlot[g, communities, VertexStyle -> PropertyValue[g, VertexStyle]]
Add the option
Method -> "Hierarchical"
to get
5
When you construct a Graph using the syntax Graph[edgelist, options] the list of vertices is taken from the edges. Using this syntax it would be impossible to add an edge-less vertex. When you refer to this nonexistent vertex in the VertexLabels option, it is an error. Then Graph fails to give a message and return unevaluated.
Use this syntax instead,
...
4
Update:
ClearAll[grapH, combinedGraph]
grapH[mat_, dir_: "Column"][t_, v_, opts : OptionsPattern[Graph]] :=
Module[{vertices = CharacterRange["A", "Z"][[;; Length@mat]],
comp = dir /. {"Column" -> VertexInComponent, "Row" -> VertexOutComponent},
gf = dir /. {"Column" -> AdjacencyGraph, "Row" -> ReverseGraph@*AdjacencyGraph}, g}...
3
You can use older GraphPlot. In version 12.0, it is renamed GraphComputation`GraphPlotLegacy.
GraphComputation`GraphPlotLegacy[{{1 -> 2, "a"}, {1 -> 2, "b"},{2 -> 1,"c"}},
DirectedEdges -> True, VertexLabeling -> True]
4
You can also use
CommunityGraphPlot[g, VertexStyle -> PropertyValue[g, VertexStyle]]
0
> CommunityGraphPlot[g, VertexStyle -> {NS | N1 | NS | N11 | NS | N18
> | NS | N24 | NS | N27 |
> NS | N35 | NS | N37 | N1 | N4 | N1 | N5 | N1 | N6 | N1 | N7 |
> N1 | N8 | N1 | N9 | N2 | N5 | N3 | N5 | N3 | N15 | N4 | N2 ->
> Red, N4 | N3 | N4 | N5 | N4 | N12 | N4 | N13 | N4 | N14 | N5 |
> N15 | N5 | N16 | N5 |...
6
You can use rules for setting values for the option VertexSize :
Graph[e, VertexSize -> {v_ -> .6, v_ /; Length[v] === 4 -> .9},
PerformanceGoal -> "Quality", DirectedEdges -> True,
VertexLabels -> Placed["Name", Center],
ImageSize -> 1500, BaseStyle -> {"Arrowheads" -> .009}]
Alternatively,
Graph[e, VertexSize -> {v_ :&...
5
Clear["Global`*"]
e = {{M1, W1} -> {M1, M2, W1, W2}, {M1, W2} -> {M1, M2, W1, W2}, {M1,
W3} -> {M1, M3, W3, W4}, {M1, W4} -> {M1, M3, W3, W4}, {M2,
W1} -> {M1, M2, W1, W2}, {M2, W1} -> {M2, M3, W1, W2}, {M2,
W2} -> {M1, M2, W1, W2}, {M2, W2} -> {M2, M3, W1, W2}, {M2,
W3} -> {M2, M3, W3, W4}, {M2, W4} -> {...
6
One possibility is to use a VertexShapeFunction whose size depends on the length of the vertex name:
Graph[
e,
PerformanceGoal->"Quality",
DirectedEdges->True,
VertexLabels->Placed["Name",Center],
ImageSize->1500,
BaseStyle->{"Arrowheads"->.009},
VertexShapeFunction->Function@{Disk[#, Length[#2]/8.5], Text[#2,...
4
The GraphEmbedding function. ${}$
2
You can modify the Arrowheads setting by giving Graph a BaseStyle option:
e = {{M1, W1} -> {M1, M2, W1, W2}, {M1, W2} -> {M1, M2, W1,
W2}, {M1, W3} -> {M1, M3, W3, W4}, {M1, W4} -> {M1, M3, W3,
W4}, {M2, W1} -> {M1, M2, W1, W2}, {M2, W1} -> {M2, M3, W1,
W2}, {M2, W2} -> {M1, M2, W1, W2}, {M2, W2} -> {M2, M3, W1,
...
4
Reversing the graph and reformatting the nodes should get you started:
ClearAll[hasseF]
vf[{xc_, yc_}, name_, {w_, h_}] := Text[Grid[name, Dividers -> {False, True}], {xc, yc}];
hasseF = ReverseGraph@*TransitiveReductionGraph@*RelationGraph
hasseF[
SubsetQ,
Subsets[{{M1, W1}, {M1, W2}, {M2, W1}, {M2, W2}}],
VertexShapeFunction -> vf
]
Edit:
@...
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