gtest=UndirectedGraph[Rule@@@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},10,"FinalState"]]
In[]:=
Out[]=
MeanDegreeConnectivity[gtest]
In[]:=
0,4,4,
2693
531
,
811
196
,
1127
265
,
305
78
,
61
14
,
143
32
,
73
18
,
41
10
,
13
3

Out[]=
N[%]
In[]:=
{0.,4.,4.,5.07156,4.13776,4.25283,3.91026,4.35714,4.46875,4.05556,4.1,4.33333}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
LocalClusteringCoefficient[gtest]
In[]:=
Out[]=
Histogram[%]
In[]:=
Out[]=
Histogram[LocalClusteringCoefficient[UndirectedGraph[Rule@@@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"FinalState"]]]]
In[]:=
MeanClusteringCoefficient[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
0,
7
12
,
3
5
,
61
105
,
68
165
,
19
54
,
31
100
,
163
540
,
35101
120960
,
17231
55755
,
256673
895356
,
198719
680295
,
888731
3094520
,
206447179
715314600
,
6428525797
22329707400

Out[]=
N[%]
In[]:=
{0.,0.583333,0.6,0.580952,0.412121,0.351852,0.31,0.301852,0.290187,0.309049,0.286671,0.292107,0.287195,0.28861,0.287891}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
GlobalClusteringCoefficient[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
0,
3
5
,
6
11
,
1
2
,
3
10
,
27
97
,
15
61
,
28
117
,
153
653
,
303
1219
,
105
454
,
246
1043
,
894
3869
,
366
1585
,
3015
13129

Out[]=
N[%]
In[]:=
{0.,0.6,0.545455,0.5,0.3,0.278351,0.245902,0.239316,0.234303,0.248564,0.231278,0.235858,0.231067,0.230915,0.229644}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
GraphReciprocity[Rule@@@#]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
Out[]=
GraphAssortativity[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
-1,-
5
7
,-
5
7
,-
7
18
,-
40
113
,-
289
1663
,-
1289
7503
,-
143
753
,-
22021
112587
,-
88061
393889
,-
114701
742690
,-
477748
2637461
,-
715321
4796999
,-
3456607
22737501
,-
3400486
23750793

Out[]=
N[%]
In[]:=
{-1.,-0.714286,-0.714286,-0.388889,-0.353982,-0.173782,-0.171798,-0.189907,-0.195591,-0.223568,-0.15444,-0.181139,-0.149118,-0.152022,-0.143174}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
MeanNeighborDegree[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
Out[]=
GraphDiameter[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
{2,2,2,3,4,6,6,8,10,12,15,19,24,30,37}
Out[]=
ListLinePlot[%140]
In[]:=
Out[]=
GraphRadius[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
{1,1,1,2,2,3,4,5,6,8,9,12,15,19,23}
Out[]=
GraphRadius[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{0,0},{0,0}},14,"StatesList"]
In[]:=
{0,1,1,2,2,3,4,5,6,8,10,13,16,20,26}
Out[]=
LogDifferences[%140]//N
In[]:=
{0.,0.,1.40942,1.28922,2.2239,0.,2.15442,1.89453,1.73045,2.34124,2.71676,2.91863,3.01106,3.03974}
Out[]=
VertexCount[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
{3,4,5,7,11,18,30,54,96,177,323,589,1082,1985,3645}
Out[]=
Log[%140,%141]//N
In[]:=
{1.58496,2.,2.32193,1.77124,1.72972,1.61315,1.89824,1.9183,1.98227,2.08304,2.13351,2.16626,2.19838,2.23256,2.2712}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
EdgeCount[UndirectedGraph[Rule@@@#]]&/@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},14,"StatesList"]
In[]:=
{2,4,6,10,18,32,56,104,188,350,642,1174,2160,3966,7286}
Out[]=
%142/%141//N
In[]:=
{0.666667,1.,1.2,1.42857,1.63636,1.77778,1.86667,1.92593,1.95833,1.9774,1.98762,1.99321,1.9963,1.99798,1.9989}
Out[]=
​
{3,4,5,7,11,18,30,54,96,177,323,589,1082,1985,3645}
Graph[g,VertexStyleRed,EdgeStyleLightGray,opts,VertexSize((#2ld[#][[r]])&/@VertexList[g]),PlotTheme"Default"]]
gtest=UndirectedGraph[Rule@@@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},10,"FinalState"]]
In[]:=
Out[]=
Histogram[#[gtest]]&/@{ClosenessCentrality,BetweennessCentrality,DegreeCentrality,EigenvectorCentrality}
In[]:=
Out[]=
Histogram[#[Last[gglist]]]&/@{ClosenessCentrality,BetweennessCentrality,DegreeCentrality,EigenvectorCentrality}
In[]:=
Out[]=
Histogram[ClosenessCentrality[#]]&/@gglist
In[]:=
Out[]=
Histogram[BetweennessCentrality[#]]&/@gglist
In[]:=
Out[]=
BetweennessCentrality[gtest]
In[]:=
VertexList[gtest]
In[]:=
With[{cc=BetweennessCentrality[gtest]},Graph[gtest,VertexSizeThread[VertexList[gtest]12*(cc/Max[cc])]]]
In[]:=
Out[]=
Clear[cent]
In[]:=
cent[f_,gtest_,mult_:12]:=With[{cc=f[gtest]},Graph[gtest,VertexStyleRed,VertexSizeThread[VertexList[gtest]mult*(cc/Max[cc])]]]
In[]:=
cent[#,gtest]&/@{BetweennessCentrality,DegreeCentrality,EigenvectorCentrality}
In[]:=
Out[]=
cent[LocalClusteringCoefficient,gtest]
In[]:=
Out[]=
cent[VertexDegree,gtest]
In[]:=
Out[]=
gglist[[-2]]
In[]:=
Out[]=
UndirectedGraphQ[%187]
In[]:=
True
Out[]=
cent[#,%187,2]&/@{BetweennessCentrality,DegreeCentrality,EigenvectorCentrality}
In[]:=
Out[]=
With[{cc=ClosenessCentrality[gtest]},Graph[gtest,VertexSizeThread[VertexList[gtest]5*(cc/Max[cc])]]]
In[]:=
Out[]=
gtest