VChanges[g_]:=Module[{vrall=GraphNeighborhoodVolumes[g,All,Automatic]},Association[Function[{v},vMean[(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],VertexStyleNormal[%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}],PlotRange4]
In[]:=
Out[]=
MeshConnectivityGraph[BoundaryMesh[DiscretizeGraphics[Ellipsoid[{0,0,0},{1,2,3}]]]]
In[]:=
Out[]=
GraphPlot3D[%177,GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic]
In[]:=
Out[]=
​
ContourPlot3D[x^2+2y^2+z^26,{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