Estime the frequency of knobs in random graphs....
XKnobs[Random3Graph[20]]
{{2, 13, 16}, {5}, {8}, {9}}
XKnobs[Random3Graph[100]]
{{19}, {22}, {23}, {26}, {46}, {49}, {51}, {52}, {55},
{64}, {71}, {73}, {76}, {88}, {97}}
{64}, {71}, {73}, {76}, {88}, {97}}
XKnobs[Random3Graph[100]]
{{8}, {19}, {34}, {37}, {41}, {43}, {45}, {65}, {70},
{78}, {81}, {82}}
{78}, {81}, {82}}
XKnobs[Random3Graph[100]]
{{9}, {10}, {16}, {17}, {23}, {25}, {39}, {46}, {53},
{55}, {57}, {63}, {83}, {86}, {88}, {91}}
{55}, {57}, {63}, {83}, {86}, {88}, {91}}
XKnobs[Random3Graph[100]]
{{3}, {9}, {10}, {38, 47}, {69}, {72}, {80}, {89}, {92},
{94}, {95}}
{94}, {95}}
XKnobs[Random3Graph[100]]
{{18}, {20}, {24}, {25}, {31}, {32}, {50}, {55}, {59},
{61}, {82}, {86}, {93}, {100}}
{61}, {82}, {86}, {93}, {100}}
Table[XKnobs[Random3Graph[10]],{10}]
{{{5}, {6}}, {{5}, {6}, {10}}, {{4}}, {{3}, {6}},
{{1}, {2}, {3}}, {{6}, {7}, {10}}, {{1}, {7}},
{{4, 10}, {5}, {8}, {9}}, {{3, 4}, {10}}, {{7}, {10}}}
{{1}, {2}, {3}}, {{6}, {7}, {10}}, {{1}, {7}},
{{4, 10}, {5}, {8}, {9}}, {{3, 4}, {10}}, {{7}, {10}}}
Length[%302]
14
f[n_]:=Plus@@Table[Length[XKnobs[Random3Graph[n]]],{40}]
1
40.
f[10]
1.85
f[20]
2.75
Table[{i,f[i]},{i,5,40,5}]
{{5, 1.525}, {10, 2.125}, {15, 2.775}, {20, 3.275},
{25, 3.925}, {30, 4.225}, {35, 5.35}, {40, 5.3}}
{25, 3.925}, {30, 4.225}, {35, 5.35}, {40, 5.3}}
ListPlot[%,PlotJoinedTrue];
Table[{i,f[i]},{i,10,100,10}]
{{10, 1.975}, {20, 3.1}, {30, 4.125}, {40, 5.475},
{50, 7.2}, {60, 7.775}, {70, 9.525}, {80, 10.75},
{90, 11.3}, {100, 11.825}}
{50, 7.2}, {60, 7.775}, {70, 9.525}, {80, 10.75},
{90, 11.3}, {100, 11.825}}
ListPlot[%,PlotJoinedTrue];
f[n_]:=Plus@@Table[Length[XKnobs[Random3Graph[n]]],{100}]
1
100.
Table[{i,f[i]},{i,10,200,20}]
{{10, 1.75}, {30, 4.2}, {50, 6.63}, {70, 9.27},
{90, 11.81}, {110, 14.42}, {130, 16.7}, {150, 19.28},
{170, 22.07}, {190, 24.24}}
{90, 11.81}, {110, 14.42}, {130, 16.7}, {150, 19.28},
{170, 22.07}, {190, 24.24}}
ListPlot[%,PlotJoinedTrue];
Fit[%320,{1,x},x]
0.441545 + 0.125955 x
g[n_]:=Plus@@TableWith{x=XKnobs[Random3Graph[n]]},,{100}
1
100.
Plus@@Length/@x
Length[x]
g[10]
1.68667
Table[{i,g[i]},{i,10,200,20}]
{{10, 1.42333}, {30, 1.08179}, {50, 1.06037},
{70, 1.05997}, {90, 1.035}, {110, 1.01092},
{130, 1.02323}, {150, 1.01327}, {170, 1.01892},
{190, 1.00758}}
{70, 1.05997}, {90, 1.035}, {110, 1.01092},
{130, 1.02323}, {150, 1.01327}, {170, 1.01892},
{190, 1.00758}}
ListPlot[%,PlotJoinedTrue];
ListPlot[Log[%%-1],PlotJoinedTrue];
Random3Graph[200];
XKnobs[%]
{{6}, {35}, {41}, {52}, {57}, {73}, {79}, {93}, {94},
{96}, {103}, {104}, {107}, {114}, {117}, {118}, {124},
{127}, {134}, {143}, {147}, {148}, {164}, {167},
{174}, {199}}
{96}, {103}, {104}, {107}, {114}, {117}, {118}, {124},
{127}, {134}, {143}, {147}, {148}, {164}, {167},
{174}, {199}}
{{52, 52}, {73, 73}, {157, 157}}
2
{0, 2, 1, 1, 1, 3, 1, 0, 1, 0}
{0, 0, 1, 1, 0, 2, 0, 1, 0, 1}
{0, 0, 0, 1, 2, 2, 1, 3, 1, 0, 2, 2, 0, 2, 0, 3, 1, 0,
0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 3, 1, 1, 0, 0, 1, 0, 1,
0, 1, 3, 1, 0, 1, 0, 0, 0, 4, 0, 1, 1, 2}
0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 3, 1, 1, 0, 0, 1, 0, 1,
0, 1, 3, 1, 0, 1, 0, 0, 0, 4, 0, 1, 1, 2}
1.02
1.14