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VChanges[g_]:=Module[{vrall=GraphNeighborhoodVolumes[g,All,Automatic]},Association[Function[{v},vMean[(vrall[#]-vrall[v])&/@Complement[VertexList[NeighborhoodGraph[g,v,1]],{v}]]]/@VertexList[g]]]
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VChanges[gtest]
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This is the average growth rate of the area of a circle at a position on the ellipsoid