TransitivityTest[g_]:=Position[GraphDistanceMatrix[g],1]
{{a,b},{b,c},{a,c}}
GraphDistanceMatrix
In[]:=
Out[]=
LengthFindClique
,{3},All
In[]:=
120
Out[]=
BinomialVertexCount,3
In[]:=
374660
Out[]=
LocalClusteringCoefficient
In[]:=
Out[]=
Histogram[%]
In[]:=
Out[]=
MultiwaySystem[{"A""AB","B""A"},"A",8,"BranchialGraphStructure"]
In[]:=
Out[]=
LocalClusteringCoefficient[%]
In[]:=
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1
34
45
17
26
5
8
3
5
5
8
88
153
3
5
9
13
5
8
5
8
17
26
58
91
5
9
82
153
73
120
23
42
7
12
83
153
18
35
23
42
4
7
83
153
82
153
15
22
73
120
3
5
73
120
5
9
3
5
58
91
3
5
73
120
15
22
Out[]=
Histogram[%]
In[]:=
Out[]=
FindClique[,{3},All]
In[]:=
{}
Out[]=
GraphDistanceMatrix
In[]:=
Out[]=
GlobalClusteringCoefficient
In[]:=
2427
4102
Out[]=
N[%]
In[]:=
0.591663
Out[]=
MultiwaySystem[{"""A","""B"},"",6,"BranchialGraph"]//GlobalClusteringCoefficient
In[]:=
796
1537
Out[]=
N[%]
In[]:=
0.517892
Out[]=
First/@Gather[ParallelMapMonitored[Catch[Module[{u},Do[u=MultiwaySystem[#,"A",t,"BranchialGraphStructure"];If[VertexCount[u]>150||EdgeCount[u]>150,Throw[u]],{t,9}];u]]#&,Catenate[allrules]],IsomorphicGraphQ[First[#],First[#2]]&]
In[]:=
Out[]=
[[ Can look at global clustering coefficient
N[GlobalClusteringCoefficient[First[#]]]Last[#]&/@%
In[]:=
Out[]=
SortBy[%,First]
In[]:=
Out[]=
Table[GlobalClusteringCoefficient[MultiwaySystem[{"A""AB","B""A"},"A",t,"BranchialGraphStructure"]],{t,15}]
In[]:=
0,0,1,,,,,,,,,,,,
7
8
93
113
105
142
921
1391
2427
4102
5949
11218
4603
9640
488
1129
33111
84152
69441
192821
15829
47772
191281
624387
Out[]=
N[%]
In[]:=
{0.,0.,1.,0.875,0.823009,0.739437,0.662114,0.591663,0.530308,0.47749,0.432241,0.393467,0.360132,0.331345,0.30635}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
ParallelTable[Echo@GlobalClusteringCoefficient[MultiwaySystem[{"A""AB","B""A"},"A",t,"BranchialGraphStructure"]],{t,20}]
In[]:=
>> 0
(kernel 84)
>> 0
(kernel 83)
>> 1
(kernel 82)
>>
7
8
(kernel 81)
>>
93
113
(kernel 80)
>>
105
142
(kernel 79)
>>
921
1391
(kernel 78)
>>
2427
4102
(kernel 77)
>>
5949
11218
(kernel 76)
>>
4603
9640
(kernel 75)
>>
488
1129
(kernel 74)
>>
33111
84152
(kernel 73)
>>
69441
192821
(kernel 72)
>>
15829
47772
(kernel 71)
>>
191281
624387
(kernel 70)
>>
1137753
3998768
(kernel 69)
>>
741853
2795643
(kernel 68)
>>
4302561
17318650
(kernel 67)
Table[GlobalClusteringCoefficient[MultiwaySystem[{"""A","""B"},"",t,"BranchialGraph"]],{t,12}]
In[]:=
0,,,,,,,,,,,
3
4
27
38
50
77
216
371
796
1537
2634
5719
24222
58903
70164
189977
64880
194313
57986
190837
453790
1630901
Out[]=
N[%]
In[]:=
{0.,0.75,0.710526,0.649351,0.58221,0.517892,0.46057,0.411218,0.369329,0.333894,0.303851,0.278245}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
Out[]=
Show[%,%%]
In[]:=
Out[]=
Global clustering coefficients seem to gradually decrease with size....
Global clustering coefficients seem to gradually decrease with size....
Ball sizes
Ball sizes
ParallelTable[With[{q=MultiwaySystem[{"""A","""B"},"A",t,"BranchialGraphStructure"]},RaggedMeanAround[Values[GraphNeighborhoodVolumes[q]]]],{t,2,10}]
In[]:=
Out[]=
PadRight[{{1,5.3±0.5,7},{1,8.5±0.6,14.20±0.30,15},{1,12.6±0.6,26.7±0.6,30.50±0.20,31},{1,17.7±0.6,47.8±1.0,60.2±0.5,62.57±0.18,63},{1,23.8±0.5,82.0±1.5,115.9±1.0,125.1±0.4,126.62±0.16,127},{1,30.9±0.5,135.5±1.9,218.9±1.8,247.4±0.8,253.32±0.33,254.66±0.15,255},{1,38.9±0.4,215.7±2.4,404.7±2.9,484.2±1.6,505.5±0.6,509.49±0.29,510.69±0.14,511},{1,47.95±0.34,331.6±2.7,731.±4.,938.8±2.9,1003.8±1.2,1018.1±0.5,1021.63±0.26,1022.71±0.13,1023},{1,57.97±0.28,493.8±3.0,1289.±6.,1801.±5.,1983.4±2.3,2032.8±0.9,2042.6±0.5,2045.74±0.24,2046.73±0.12,2047}},Automatic,None]
In[]:=
Out[]=
Transpose[%73]
In[]:=
Out[]=
MapIndexed[{#2[[2]],#}&,%,{2}]
In[]:=
Out[]=
DeleteCases[%77,{_,None},{2}]
In[]:=
Out[]=
ListLogPlot[%,JoinedTrue]
In[]:=
Out[]=
DeleteCases[%76,None,{2}]
In[]:=
Out[]=
Ratios/@%
In[]:=
Out[]=
%82
In[]:=
Out[]=
ListLinePlot[Most[%82]]
In[]:=
Out[]=
Table[GraphDiameter[MultiwaySystem[{"""A","""B"},"A",t,"BranchialGraphStructure"]],{t,8}]
In[]:=
{1,2,3,4,5,6,7,8}
Out[]=
Ratios[Table[N@Mean@VertexDegree[MultiwaySystem[{"""A","""B"},"A",t,"BranchialGraphStructure"]],{t,8}]]
In[]:=
{2.14286,1.74222,1.5553,1.44065,1.36394,1.30954,1.26916}
Out[]=
Table[N@Mean@VertexDegree[MultiwaySystem[{"""A","""B"},"A",t,"BranchialGraphStructure"]],{t,12}]
In[]:=
{2.,4.28571,7.46667,11.6129,16.7302,22.8189,29.8824,37.9256,46.9541,56.9722,67.9834,79.9902}
Out[]=
Ratios[%]
In[]:=
{2.14286,1.74222,1.5553,1.44065,1.36394,1.30954,1.26916,1.23806,1.21336,1.19327,1.17661}
Out[]=
ListLinePlot[%87]
In[]:=
Out[]=
ListLinePlot[%86]
In[]:=
Out[]=