In[]:=
RaggedMeanAround[Values[GraphNeighborhoodVolumes[CayleyGraph[AlternatingGroup[5]]]]]
Out[]=
{1,3,7,14,26,40,51,57,60}
In[]:=
RaggedMeanAround[Values[GraphNeighborhoodVolumes[CayleyGraph[AlternatingGroup[6]],{1}]]]
Out[]=
{1,3,7,14,27,50,88,145,217,292,342,358,360}
In[]:=
Ratios[%]//N
Out[]=
{3.,2.33333,2.,1.92857,1.85185,1.76,1.64773,1.49655,1.34562,1.17123,1.04678,1.00559}
In[]:=
RaggedMeanAround[Values[GraphNeighborhoodVolumes[CayleyGraph[AlternatingGroup[8]],{1}]]]
Out[]=
{1,3,7,14,27,51,95,175,321,585,1046,1826,3087,5053,7939,11664,15659,18707,19897,20142,20160}
In[]:=
ListLogLogPlot[%]
Out[]=