VChanges[g_]:=Module[{vrall=GraphNeighborhoodVolumes[g,All,Automatic]},Association[Function[{v},vMean[(vrall[#]-vrall[v])&/@Complement[VertexList[NeighborhoodGraph[g,v,1]],{v}]]]/@VertexList[g]]]
In[]:=
VChanges[gtest]
In[]:=
Out[]=
VChanges[TorusGraph[{5,5}]]
In[]:=
Out[]=
VChanges[BuckyballGraph[4]]
In[]:=
Out[]=
BuckyballGraph[2]
In[]:=
Out[]=
VChanges[BuckyballGraph[2]]//N
In[]:=
Out[]=
Values[%]//MatrixPlot
In[]:=
Out[]=
Mean[Values[VChanges[BuckyballGraph[2]]]]
In[]:=
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
Out[]=
#[[3]]&/@VChanges[BuckyballGraph[2]]
In[]:=
Out[]=
#[[4]]&/@VChanges[BuckyballGraph[2]]//N
In[]:=
Out[]=
If[#>0,Red,Blue]&/@(#[[4]]&/@VChanges[BuckyballGraph[2]])
In[]:=
Out[]=
GraphPlot3D[BuckyballGraph[2],VertexStyleNormal[%162],VertexSize.5]
In[]:=
Out[]=
#[[5]]&/@VChanges[BuckyballGraph[2]]//N
In[]:=
Out[]=
GraphFunctionPlot[BuckyballGraph[2],%160,GraphPlot3D,VertexSize.5]
In[]:=
Out[]=
GraphNeighborhoodVolumes[BuckyballGraph[2],All,Automatic]
In[]:=
Out[]=
Mean[Values[VChanges[gtest]]]
In[]:=
0,,,,,,,,,
554647
813960
134111
124355
145495
85272
4816589
2238390
25533047
8953560
874173
248710
3023431
813960
863897
248710
416939
159885
Out[]=
N[%]
In[]:=
{0.,0.681418,1.07845,1.70625,2.15181,2.85172,3.51483,3.71447,3.47351,2.60774}
Out[]=
Graphics3D[Ellipsoid[{0,0,0},{1,2,3}],PlotRange4]
In[]:=
Out[]=
MeshConnectivityGraph[BoundaryMesh[DiscretizeGraphics[Ellipsoid[{0,0,0},{1,2,3}]]]]
In[]:=
Out[]=
GraphPlot3D[%177,GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic]
In[]:=
Out[]=
ContourPlot3D[x^2+2y^2+z^26,{x,-3,3},{y,-3,3},{z,-3,3}]
In[]:=
Out[]=
GraphicsMetricGraph[%182,200]
In[]:=
Out[]=
GraphPlot3D[%]
In[]:=
Out[]=
Mean[Values[VChanges[%186]]]
In[]:=
0,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
2953
22686
218159
1191015
173405
635208
481097
1361160
655009
1588020
120590
238203
3893
6965
607073
952812
6567539
9528120
3652729
4764060
3895657
4764060
1181459
1361160
9012553
9528120
677447
680580
2539
2388
1170101
1058680
3714541
3176040
1642537
1361160
629579
501480
435787
340290
3119791
2382030
358349
264670
6501113
4764060
6704483
4764060
640627
453720
13566269
9528120
717989
501480
13632491
9528120
13427683
9528120
4417327
3176040
144075
105868
2525561
1905624
6133051
4764060
986071
794010
11343629
9528120
1190723
1058680
724973
680580
9483979
9528120
2924023
3176040
373537
453720
7088483
9528120
95153
151240
Out[]=
N[%]
In[]:=
{0.,0.130168,0.183171,0.272989,0.353446,0.412469,0.506249,0.558938,0.637138,0.68928,0.766726,0.817718,0.86798,0.94589,0.995397,1.06323,1.10525,1.16955,1.20672,1.25544,1.28063,1.30972,1.35395,1.36462,1.4073,1.41194,1.42381,1.43174,1.43076,1.40927,1.39083,1.36089,1.32532,1.28736,1.24189,1.19054,1.12472,1.06523,0.995367,0.920651,0.823276,0.743954,0.629152}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
This is the average growth rate of the area of a circle at a position on the ellipsoid