In[]:=
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]
Out[]=
This is the average growth rate of the area of a circle at a position on the ellipsoid