<<NetworkSystems/NewGraphs.m
Union[PermToGraph /@ Permutations[Range[6]]]
{{{1, 1}, {1, 2}, {2, 2}}, {{1, 1}, {2, 1}, {2, 2}},
{{1, 2}, {1, 2}, {1, 2}}, {{1, 2}, {1, 2}, {2, 1}},
{{1, 2}, {2, 1}, {2, 1}}, {{2, 1}, {2, 1}, {2, 1}}}
{{1, 2}, {1, 2}, {1, 2}}, {{1, 2}, {1, 2}, {2, 1}},
{{1, 2}, {2, 1}, {2, 1}}, {{2, 1}, {2, 1}, {2, 1}}}
UniqueGraphs[%]
{{{1, 1}, {1, 2}, {2, 2}}, {{1, 1}, {2, 1}, {2, 2}},
{{1, 2}, {1, 2}, {1, 2}}, {{1, 2}, {1, 2}, {2, 1}},
{{1, 2}, {2, 1}, {2, 1}}, {{2, 1}, {2, 1}, {2, 1}}}
{{1, 2}, {1, 2}, {1, 2}}, {{1, 2}, {1, 2}, {2, 1}},
{{1, 2}, {2, 1}, {2, 1}}, {{2, 1}, {2, 1}, {2, 1}}}
Apply[G, %11, {1}]
{G[{1, 1}, {1, 2}, {2, 2}], G[{1, 1}, {2, 1}, {2, 2}],
G[{1, 2}, {1, 2}, {1, 2}], G[{1, 2}, {1, 2}, {2, 1}],
G[{1, 2}, {2, 1}, {2, 1}], G[{2, 1}, {2, 1}, {2, 1}]}
G[{1, 2}, {1, 2}, {1, 2}], G[{1, 2}, {1, 2}, {2, 1}],
G[{1, 2}, {2, 1}, {2, 1}], G[{2, 1}, {2, 1}, {2, 1}]}
% /. G[{a_, b_}, {a_, b_}] -> xx
{G[{1, 1}, {1, 2}, {2, 2}], G[{1, 1}, {2, 1}, {2, 2}],
G[xx, {1, 2}], G[xx, {2, 1}], G[xx, {1, 2}],
G[xx, {2, 1}]}
G[xx, {1, 2}], G[xx, {2, 1}], G[xx, {1, 2}],
G[xx, {2, 1}]}
IrreducibleKnobs[Random3Graph[100]]
{{{6, 14}, {18, 14}, {86, 14}},
{{19, 23}, {37, 23}, {80, 23}},
{{56, 24}, {85, 24}, {100, 24}},
{{21, 27}, {55, 27}, {57, 27}},
{{34, 46}, {58, 46}, {62, 46}},
{{64, 51}, {85, 51}, {88, 51}},
{{54, 67}, {58, 67}, {76, 67}},
{{38, 69}, {71, 69}, {89, 69}},
{{29, 75}, {47, 75}, {89, 75}},
{{50, 90}, {74, 90}, {79, 90}}}
{{19, 23}, {37, 23}, {80, 23}},
{{56, 24}, {85, 24}, {100, 24}},
{{21, 27}, {55, 27}, {57, 27}},
{{34, 46}, {58, 46}, {62, 46}},
{{64, 51}, {85, 51}, {88, 51}},
{{54, 67}, {58, 67}, {76, 67}},
{{38, 69}, {71, 69}, {89, 69}},
{{29, 75}, {47, 75}, {89, 75}},
{{50, 90}, {74, 90}, {79, 90}}}
RenumberGraph /@ %
{{{1, 2}, {3, 2}, {4, 2}}, {{1, 2}, {3, 2}, {4, 2}},
{{2, 1}, {3, 1}, {4, 1}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {3, 2}, {4, 2}}, {{2, 1}, {3, 1}, {4, 1}},
{{1, 3}, {2, 3}, {4, 3}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 3}, {2, 3}, {4, 3}}, {{1, 4}, {2, 4}, {3, 4}}}
{{2, 1}, {3, 1}, {4, 1}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {3, 2}, {4, 2}}, {{2, 1}, {3, 1}, {4, 1}},
{{1, 3}, {2, 3}, {4, 3}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 3}, {2, 3}, {4, 3}}, {{1, 4}, {2, 4}, {3, 4}}}
Union[%]
{{{1, 2}, {3, 2}, {4, 2}}, {{1, 3}, {2, 3}, {4, 3}},
{{1, 4}, {2, 4}, {3, 4}}, {{2, 1}, {3, 1}, {4, 1}}}
{{1, 4}, {2, 4}, {3, 4}}, {{2, 1}, {3, 1}, {4, 1}}}
UniqueGraphs[%]
{{{1, 2}, {3, 2}, {4, 2}}, {{1, 3}, {2, 3}, {4, 3}},
{{1, 4}, {2, 4}, {3, 4}}, {{2, 1}, {3, 1}, {4, 1}}}
{{1, 4}, {2, 4}, {3, 4}}, {{2, 1}, {3, 1}, {4, 1}}}
Union[ RenumberGraph /@ IrreducibleKnobs[Random3Graph[100]]]
{{{1, 2}, {2, 2}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 3}, {2, 3}, {4, 3}}, {{1, 4}, {2, 4}, {3, 4}},
{{2, 1}, {3, 1}, {3, 1}}, {{2, 1}, {3, 1}, {4, 1}}}
{{1, 3}, {2, 3}, {4, 3}}, {{1, 4}, {2, 4}, {3, 4}},
{{2, 1}, {3, 1}, {3, 1}}, {{2, 1}, {3, 1}, {4, 1}}}
Union[CanonicalGraph /@ %115]
{{{1, 2}, {2, 2}}, {{1, 2}, {3, 2}, {3, 2}},
{{1, 2}, {3, 2}, {4, 2}}}
{{1, 2}, {3, 2}, {4, 2}}}
Union[ RenumberGraph /@ IrreducibleKnobs[Random3Graph[100]]]
{{{1, 2}, {3, 2}, {4, 2}}, {{1, 3}, {2, 3}, {4, 3}},
{{1, 4}, {2, 4}, {3, 4}}, {{2, 1}, {3, 1}, {4, 1}}}
{{1, 4}, {2, 4}, {3, 4}}, {{2, 1}, {3, 1}, {4, 1}}}
Union[CanonicalGraph /@ %116]
{{{1, 2}, {3, 2}, {4, 2}}}
BicycleGraph[n_] := Join[Table[{i, i+1}, {i, n}], Table[{i, i+1}, {i, n+1, 2n}], Table[{i + n, i}, {i, n}]]
BicycleGraph[3]
{{1, 2}, {2, 3}, {3, 1}, {4, 5}, {5, 6}, {6, 4}, {4, 1},
{5, 2}, {6, 3}}
{5, 2}, {6, 3}}
IrreducibleKnobs[%]
{{{1, 2}, {2, 3}, {3, 1}, {4, 1}, {5, 2}, {6, 3}}}
BicycleGraph[4]
{{1, 2}, {2, 3}, {3, 4}, {4, 1}, {5, 6}, {6, 7}, {7, 8},
{8, 5}, {5, 1}, {6, 2}, {7, 3}, {8, 4}}
{8, 5}, {5, 1}, {6, 2}, {7, 3}, {8, 4}}
IrreducibleKnobs[%]
{{{1, 2}, {2, 3}, {3, 4}, {4, 1}, {5, 1}, {6, 2}, {7, 3},
{8, 4}}}
{8, 4}}}
Random3Graph[40]
{{1, 32}, {1, 33}, {1, 39}, {2, 15}, {2, 23}, {3, 16},
{4, 18}, {4, 19}, {4, 30}, {5, 17}, {6, 3}, {6, 31},
{6, 38}, {7, 10}, {7, 40}, {8, 34}, {8, 36}, {10, 25},
{10, 36}, {11, 9}, {11, 20}, {12, 7}, {13, 12},
{13, 22}, {14, 24}, {15, 25}, {15, 27}, {16, 33},
{16, 40}, {17, 27}, {19, 22}, {19, 34}, {20, 35},
{21, 2}, {21, 12}, {21, 38}, {23, 9}, {23, 32},
{24, 9}, {24, 40}, {25, 26}, {26, 22}, {26, 35},
{27, 39}, {28, 38}, {29, 5}, {29, 13}, {29, 18},
{30, 3}, {30, 14}, {31, 18}, {31, 39}, {32, 28},
{33, 5}, {34, 20}, {35, 28}, {36, 17}, {37, 8},
{37, 11}, {37, 14}}
{4, 18}, {4, 19}, {4, 30}, {5, 17}, {6, 3}, {6, 31},
{6, 38}, {7, 10}, {7, 40}, {8, 34}, {8, 36}, {10, 25},
{10, 36}, {11, 9}, {11, 20}, {12, 7}, {13, 12},
{13, 22}, {14, 24}, {15, 25}, {15, 27}, {16, 33},
{16, 40}, {17, 27}, {19, 22}, {19, 34}, {20, 35},
{21, 2}, {21, 12}, {21, 38}, {23, 9}, {23, 32},
{24, 9}, {24, 40}, {25, 26}, {26, 22}, {26, 35},
{27, 39}, {28, 38}, {29, 5}, {29, 13}, {29, 18},
{30, 3}, {30, 14}, {31, 18}, {31, 39}, {32, 28},
{33, 5}, {34, 20}, {35, 28}, {36, 17}, {37, 8},
{37, 11}, {37, 14}}
IrreducibleKnobs[%]
{{{11, 9}, {23, 9}, {24, 9}},
{{4, 18}, {29, 18}, {31, 18}},
{{13, 22}, {19, 22}, {26, 22}},
{{6, 38}, {21, 38}, {28, 38}},
{{1, 39}, {27, 39}, {31, 39}},
{{7, 40}, {16, 40}, {24, 40}}}
{{4, 18}, {29, 18}, {31, 18}},
{{13, 22}, {19, 22}, {26, 22}},
{{6, 38}, {21, 38}, {28, 38}},
{{1, 39}, {27, 39}, {31, 39}},
{{7, 40}, {16, 40}, {24, 40}}}
Union[ RenumberGraph /@ % ]
{{{1, 2}, {3, 2}, {4, 2}}, {{1, 3}, {2, 3}, {4, 3}},
{{1, 4}, {2, 4}, {3, 4}}, {{2, 1}, {3, 1}, {4, 1}}}
{{1, 4}, {2, 4}, {3, 4}}, {{2, 1}, {3, 1}, {4, 1}}}
Apply[G, %131]
G[{1, 32}, {1, 33}, {1, 39}, {2, 15}, {2, 23}, {3, 16},
{4, 18}, {4, 19}, {4, 30}, {5, 17}, {6, 3}, {6, 31},
{6, 38}, {7, 10}, {7, 40}, {8, 34}, {8, 36}, {10, 25},
{10, 36}, {11, 9}, {11, 20}, {12, 7}, {13, 12},
{13, 22}, {14, 24}, {15, 25}, {15, 27}, {16, 33},
{16, 40}, {17, 27}, {19, 22}, {19, 34}, {20, 35},
{21, 2}, {21, 12}, {21, 38}, {23, 9}, {23, 32},
{24, 9}, {24, 40}, {25, 26}, {26, 22}, {26, 35},
{27, 39}, {28, 38}, {29, 5}, {29, 13}, {29, 18},
{30, 3}, {30, 14}, {31, 18}, {31, 39}, {32, 28},
{33, 5}, {34, 20}, {35, 28}, {36, 17}, {37, 8},
{37, 11}, {37, 14}]
{4, 18}, {4, 19}, {4, 30}, {5, 17}, {6, 3}, {6, 31},
{6, 38}, {7, 10}, {7, 40}, {8, 34}, {8, 36}, {10, 25},
{10, 36}, {11, 9}, {11, 20}, {12, 7}, {13, 12},
{13, 22}, {14, 24}, {15, 25}, {15, 27}, {16, 33},
{16, 40}, {17, 27}, {19, 22}, {19, 34}, {20, 35},
{21, 2}, {21, 12}, {21, 38}, {23, 9}, {23, 32},
{24, 9}, {24, 40}, {25, 26}, {26, 22}, {26, 35},
{27, 39}, {28, 38}, {29, 5}, {29, 13}, {29, 18},
{30, 3}, {30, 14}, {31, 18}, {31, 39}, {32, 28},
{33, 5}, {34, 20}, {35, 28}, {36, 17}, {37, 8},
{37, 11}, {37, 14}]
%134 //. G[{a_, b_}, {c_, b_}, {d_, b_}] -> f[{a, c, d}]
G[f[{1, 27, 31}], f[{4, 29, 31}], f[{6, 21, 28}],
f[{7, 16, 24}], f[{11, 23, 24}], f[{13, 19, 26}],
{1, 32}, {1, 33}, {2, 15}, {2, 23}, {3, 16}, {4, 19},
{4, 30}, {5, 17}, {6, 3}, {6, 31}, {7, 10}, {8, 34},
{8, 36}, {10, 25}, {10, 36}, {11, 20}, {12, 7},
{13, 12}, {14, 24}, {15, 25}, {15, 27}, {16, 33},
{17, 27}, {19, 34}, {20, 35}, {21, 2}, {21, 12},
{23, 32}, {25, 26}, {26, 35}, {29, 5}, {29, 13},
{30, 3}, {30, 14}, {32, 28}, {33, 5}, {34, 20},
{35, 28}, {36, 17}, {37, 8}, {37, 11}, {37, 14}]
f[{7, 16, 24}], f[{11, 23, 24}], f[{13, 19, 26}],
{1, 32}, {1, 33}, {2, 15}, {2, 23}, {3, 16}, {4, 19},
{4, 30}, {5, 17}, {6, 3}, {6, 31}, {7, 10}, {8, 34},
{8, 36}, {10, 25}, {10, 36}, {11, 20}, {12, 7},
{13, 12}, {14, 24}, {15, 25}, {15, 27}, {16, 33},
{17, 27}, {19, 34}, {20, 35}, {21, 2}, {21, 12},
{23, 32}, {25, 26}, {26, 35}, {29, 5}, {29, 13},
{30, 3}, {30, 14}, {32, 28}, {33, 5}, {34, 20},
{35, 28}, {36, 17}, {37, 8}, {37, 11}, {37, 14}]
ReplaceList[%134, G[{a_, b_}, {c_, b_}, {d_, b_}] -> f[{a, c, d}]]
{}
Enumerating Knobs
Enumerating Knobs
<<NetworkSystems/NewGraphs.m
AddNodes[{{{1, 1}}}]
{{{1, 2}, {2, 1}}}
AddArcs[%]
{{{1, 2}, {2, 1}, {1, 2}}, {{1, 2}, {2, 1}, {2, 1}}}
Union[CanonicalGraph /@ %]
{{{1, 2}, {2, 1}, {1, 2}}, {{1, 2}, {2, 1}, {2, 1}}}
AddNodes[%]
{{{1, 2}, {2, 1}, {1, 3}, {3, 2}},
{{1, 2}, {2, 1}, {2, 3}, {3, 1}},
{{1, 2}, {2, 3}, {1, 2}, {3, 1}},
{{1, 2}, {2, 3}, {2, 1}, {3, 1}},
{{1, 3}, {2, 1}, {1, 2}, {3, 2}},
{{1, 3}, {2, 1}, {2, 1}, {3, 2}}}
{{1, 2}, {2, 1}, {2, 3}, {3, 1}},
{{1, 2}, {2, 3}, {1, 2}, {3, 1}},
{{1, 2}, {2, 3}, {2, 1}, {3, 1}},
{{1, 3}, {2, 1}, {1, 2}, {3, 2}},
{{1, 3}, {2, 1}, {2, 1}, {3, 2}}}
Union[CanonicalGraph /@ %]
{{{1, 2}, {2, 1}, {1, 3}, {3, 2}},
{{1, 2}, {2, 1}, {2, 3}, {3, 1}},
{{1, 2}, {2, 3}, {1, 2}, {3, 1}},
{{1, 2}, {2, 3}, {2, 1}, {3, 1}},
{{1, 2}, {3, 1}, {1, 3}, {2, 3}},
{{1, 2}, {3, 1}, {3, 1}, {2, 3}}}
{{1, 2}, {2, 1}, {2, 3}, {3, 1}},
{{1, 2}, {2, 3}, {1, 2}, {3, 1}},
{{1, 2}, {2, 3}, {2, 1}, {3, 1}},
{{1, 2}, {3, 1}, {1, 3}, {2, 3}},
{{1, 2}, {3, 1}, {3, 1}, {2, 3}}}
AddArcs[%]
{}
AddNodes[%67]
{{{1, 2}, {2, 1}, {1, 3}, {3, 4}, {4, 2}},
{{1, 2}, {2, 1}, {1, 4}, {3, 2}, {4, 3}},
{{1, 2}, {2, 1}, {2, 3}, {3, 4}, {4, 1}},
{{1, 2}, {2, 1}, {2, 4}, {3, 1}, {4, 3}},
{{1, 2}, {2, 3}, {1, 2}, {3, 4}, {4, 1}},
{{1, 2}, {2, 3}, {1, 4}, {3, 1}, {4, 2}},
{{1, 2}, {2, 3}, {2, 1}, {3, 4}, {4, 1}},
{{1, 2}, {2, 3}, {2, 4}, {3, 1}, {4, 1}},
{{1, 2}, {2, 4}, {1, 2}, {3, 1}, {4, 3}},
{{1, 2}, {2, 4}, {1, 3}, {3, 2}, {4, 1}},
{{1, 2}, {2, 4}, {2, 1}, {3, 1}, {4, 3}},
{{1, 2}, {2, 4}, {2, 3}, {3, 1}, {4, 1}},
{{1, 2}, {3, 1}, {1, 3}, {2, 4}, {4, 3}},
{{1, 2}, {3, 1}, {1, 4}, {2, 3}, {4, 3}},
{{1, 2}, {3, 1}, {3, 1}, {2, 4}, {4, 3}},
{{1, 2}, {3, 1}, {3, 4}, {2, 3}, {4, 1}},
{{1, 2}, {3, 4}, {1, 3}, {2, 3}, {4, 1}},
{{1, 2}, {3, 4}, {3, 1}, {2, 3}, {4, 1}},
{{1, 4}, {2, 1}, {1, 3}, {3, 2}, {4, 2}},
{{1, 4}, {2, 1}, {2, 3}, {3, 1}, {4, 2}},
{{1, 4}, {2, 3}, {1, 2}, {3, 1}, {4, 2}},
{{1, 4}, {2, 3}, {2, 1}, {3, 1}, {4, 2}},
{{1, 4}, {3, 1}, {1, 3}, {2, 3}, {4, 2}},
{{1, 4}, {3, 1}, {3, 1}, {2, 3}, {4, 2}}}
{{1, 2}, {2, 1}, {1, 4}, {3, 2}, {4, 3}},
{{1, 2}, {2, 1}, {2, 3}, {3, 4}, {4, 1}},
{{1, 2}, {2, 1}, {2, 4}, {3, 1}, {4, 3}},
{{1, 2}, {2, 3}, {1, 2}, {3, 4}, {4, 1}},
{{1, 2}, {2, 3}, {1, 4}, {3, 1}, {4, 2}},
{{1, 2}, {2, 3}, {2, 1}, {3, 4}, {4, 1}},
{{1, 2}, {2, 3}, {2, 4}, {3, 1}, {4, 1}},
{{1, 2}, {2, 4}, {1, 2}, {3, 1}, {4, 3}},
{{1, 2}, {2, 4}, {1, 3}, {3, 2}, {4, 1}},
{{1, 2}, {2, 4}, {2, 1}, {3, 1}, {4, 3}},
{{1, 2}, {2, 4}, {2, 3}, {3, 1}, {4, 1}},
{{1, 2}, {3, 1}, {1, 3}, {2, 4}, {4, 3}},
{{1, 2}, {3, 1}, {1, 4}, {2, 3}, {4, 3}},
{{1, 2}, {3, 1}, {3, 1}, {2, 4}, {4, 3}},
{{1, 2}, {3, 1}, {3, 4}, {2, 3}, {4, 1}},
{{1, 2}, {3, 4}, {1, 3}, {2, 3}, {4, 1}},
{{1, 2}, {3, 4}, {3, 1}, {2, 3}, {4, 1}},
{{1, 4}, {2, 1}, {1, 3}, {3, 2}, {4, 2}},
{{1, 4}, {2, 1}, {2, 3}, {3, 1}, {4, 2}},
{{1, 4}, {2, 3}, {1, 2}, {3, 1}, {4, 2}},
{{1, 4}, {2, 3}, {2, 1}, {3, 1}, {4, 2}},
{{1, 4}, {3, 1}, {1, 3}, {2, 3}, {4, 2}},
{{1, 4}, {3, 1}, {3, 1}, {2, 3}, {4, 2}}}
Union[CanonicalGraph /@ %]
{{{1, 2}, {2, 1}, {1, 3}, {3, 4}, {4, 2}},
{{1, 2}, {2, 1}, {1, 3}, {4, 2}, {3, 4}},
{{1, 2}, {2, 1}, {2, 3}, {3, 4}, {4, 1}},
{{1, 2}, {2, 1}, {2, 3}, {4, 1}, {3, 4}},
{{1, 2}, {2, 3}, {1, 2}, {3, 4}, {4, 1}},
{{1, 2}, {2, 3}, {1, 2}, {4, 1}, {3, 4}},
{{1, 2}, {2, 3}, {1, 4}, {3, 1}, {4, 2}},
{{1, 2}, {2, 3}, {1, 4}, {4, 2}, {3, 1}},
{{1, 2}, {2, 3}, {2, 1}, {3, 4}, {4, 1}},
{{1, 2}, {2, 3}, {2, 1}, {4, 1}, {3, 4}},
{{1, 2}, {2, 3}, {2, 4}, {3, 1}, {4, 1}},
{{1, 2}, {2, 3}, {2, 4}, {4, 1}, {3, 1}},
{{1, 2}, {3, 1}, {1, 3}, {2, 4}, {4, 3}},
{{1, 2}, {3, 1}, {1, 3}, {4, 3}, {2, 4}},
{{1, 2}, {3, 1}, {1, 4}, {2, 3}, {4, 3}},
{{1, 2}, {3, 1}, {1, 4}, {4, 3}, {2, 3}},
{{1, 2}, {3, 1}, {3, 1}, {2, 4}, {4, 3}},
{{1, 2}, {3, 1}, {3, 1}, {4, 3}, {2, 4}},
{{1, 2}, {3, 1}, {3, 4}, {2, 3}, {4, 1}},
{{1, 2}, {3, 1}, {3, 4}, {4, 1}, {2, 3}},
{{1, 2}, {3, 4}, {1, 3}, {2, 3}, {4, 1}},
{{1, 2}, {3, 4}, {1, 3}, {4, 1}, {2, 3}},
{{1, 2}, {3, 4}, {3, 1}, {2, 3}, {4, 1}},
{{1, 2}, {3, 4}, {3, 1}, {4, 1}, {2, 3}}}
{{1, 2}, {2, 1}, {1, 3}, {4, 2}, {3, 4}},
{{1, 2}, {2, 1}, {2, 3}, {3, 4}, {4, 1}},
{{1, 2}, {2, 1}, {2, 3}, {4, 1}, {3, 4}},
{{1, 2}, {2, 3}, {1, 2}, {3, 4}, {4, 1}},
{{1, 2}, {2, 3}, {1, 2}, {4, 1}, {3, 4}},
{{1, 2}, {2, 3}, {1, 4}, {3, 1}, {4, 2}},
{{1, 2}, {2, 3}, {1, 4}, {4, 2}, {3, 1}},
{{1, 2}, {2, 3}, {2, 1}, {3, 4}, {4, 1}},
{{1, 2}, {2, 3}, {2, 1}, {4, 1}, {3, 4}},
{{1, 2}, {2, 3}, {2, 4}, {3, 1}, {4, 1}},
{{1, 2}, {2, 3}, {2, 4}, {4, 1}, {3, 1}},
{{1, 2}, {3, 1}, {1, 3}, {2, 4}, {4, 3}},
{{1, 2}, {3, 1}, {1, 3}, {4, 3}, {2, 4}},
{{1, 2}, {3, 1}, {1, 4}, {2, 3}, {4, 3}},
{{1, 2}, {3, 1}, {1, 4}, {4, 3}, {2, 3}},
{{1, 2}, {3, 1}, {3, 1}, {2, 4}, {4, 3}},
{{1, 2}, {3, 1}, {3, 1}, {4, 3}, {2, 4}},
{{1, 2}, {3, 1}, {3, 4}, {2, 3}, {4, 1}},
{{1, 2}, {3, 1}, {3, 4}, {4, 1}, {2, 3}},
{{1, 2}, {3, 4}, {1, 3}, {2, 3}, {4, 1}},
{{1, 2}, {3, 4}, {1, 3}, {4, 1}, {2, 3}},
{{1, 2}, {3, 4}, {3, 1}, {2, 3}, {4, 1}},
{{1, 2}, {3, 4}, {3, 1}, {4, 1}, {2, 3}}}
Valences /@ %70
{{3, 3, 2, 2}, {3, 3, 2, 2}, {3, 3, 2, 2}, {3, 3, 2, 2},
{3, 3, 2, 2}, {3, 3, 2, 2}, {3, 3, 2, 2},
{3, 3, 2, 2}, {3, 3, 2, 2}, {3, 3, 2, 2},
{3, 3, 2, 2}, {3, 3, 2, 2}, {3, 2, 3, 2},
{3, 2, 3, 2}, {3, 2, 3, 2}, {3, 2, 3, 2},
{3, 2, 3, 2}, {3, 2, 3, 2}, {3, 2, 3, 2},
{3, 2, 3, 2}, {3, 2, 3, 2}, {3, 2, 3, 2},
{3, 2, 3, 2}, {3, 2, 3, 2}}
{3, 3, 2, 2}, {3, 3, 2, 2}, {3, 3, 2, 2},
{3, 3, 2, 2}, {3, 3, 2, 2}, {3, 3, 2, 2},
{3, 3, 2, 2}, {3, 3, 2, 2}, {3, 2, 3, 2},
{3, 2, 3, 2}, {3, 2, 3, 2}, {3, 2, 3, 2},
{3, 2, 3, 2}, {3, 2, 3, 2}, {3, 2, 3, 2},
{3, 2, 3, 2}, {3, 2, 3, 2}, {3, 2, 3, 2},
{3, 2, 3, 2}, {3, 2, 3, 2}}
Test Evolutions
Test Evolutions
<<NetworkSystems/NewGraphs.m
GraphEvolveList[knobruleA, mingraphB, 3]
{{{1, 1}, {1, 2}, {2, 2}}, {{1, 1}, {1, 2}, {2, 2}},
{{1, 1}, {1, 2}, {2, 2}}, {{1, 1}, {1, 2}, {2, 2}}}
{{1, 1}, {1, 2}, {2, 2}}, {{1, 1}, {1, 2}, {2, 2}}}
GraphEvolveList[knobruleA, mingraphA, 3]
{{{1, 2}, {1, 2}, {1, 2}},
{{3, 1}, {3, 2}, {3, 6}, {4, 1}, {4, 2}, {4, 6},
{5, 1}, {5, 2}, {5, 6}},
{{3, 2}, {3, 6}, {4, 2}, {4, 6}, {5, 2}, {5, 6},
{7, 1}, {7, 3}, {7, 10}, {8, 1}, {8, 4}, {8, 10},
{9, 1}, {9, 5}, {9, 10}},
{{3, 6}, {4, 6}, {5, 6}, {7, 1}, {7, 3}, {7, 10},
{8, 1}, {8, 4}, {8, 10}, {9, 1}, {9, 5}, {9, 10},
{11, 2}, {11, 3}, {11, 14}, {12, 2}, {12, 4},
{12, 14}, {13, 2}, {13, 5}, {13, 14}}}
{{3, 1}, {3, 2}, {3, 6}, {4, 1}, {4, 2}, {4, 6},
{5, 1}, {5, 2}, {5, 6}},
{{3, 2}, {3, 6}, {4, 2}, {4, 6}, {5, 2}, {5, 6},
{7, 1}, {7, 3}, {7, 10}, {8, 1}, {8, 4}, {8, 10},
{9, 1}, {9, 5}, {9, 10}},
{{3, 6}, {4, 6}, {5, 6}, {7, 1}, {7, 3}, {7, 10},
{8, 1}, {8, 4}, {8, 10}, {9, 1}, {9, 5}, {9, 10},
{11, 2}, {11, 3}, {11, 14}, {12, 2}, {12, 4},
{12, 14}, {13, 2}, {13, 5}, {13, 14}}}
Valences /@ %
{{3, 3}, {3, 3, 3, 3, 3, 3},
{3, 3, 3, 3, 3, 3, 3, 3, 3, 3},
{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}}
{3, 3, 3, 3, 3, 3, 3, 3, 3, 3},
{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}}
Length /@ GraphEvolveList[knobruleA, mingraphA, 7]
{3, 9, 15, 21, 27, 33, 39, 45}
Last[%4]
{{3, 6}, {4, 6}, {5, 6}, {7, 1}, {7, 3}, {7, 10},
{8, 1}, {8, 4}, {8, 10}, {9, 1}, {9, 5}, {9, 10},
{11, 2}, {11, 3}, {11, 14}, {12, 2}, {12, 4},
{12, 14}, {13, 2}, {13, 5}, {13, 14}}
{8, 1}, {8, 4}, {8, 10}, {9, 1}, {9, 5}, {9, 10},
{11, 2}, {11, 3}, {11, 14}, {12, 2}, {12, 4},
{12, 14}, {13, 2}, {13, 5}, {13, 14}}
GraphKnobs[%7]
{{{1, 2}, {3, 2}, {4, 2}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {3, 2}, {4, 2}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {3, 2}, {4, 2}}}
{{1, 2}, {3, 2}, {4, 2}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {3, 2}, {4, 2}}}
Union[%]
{{{1, 2}, {3, 2}, {4, 2}}}
(This demonstrates that the only knobs generated are the kind used in the rule....)
GraphEvolveList[knobruleA, tetragraph, 3]
{{{1, 4}, {1, 2}, {2, 4}, {2, 3}, {3, 4}, {3, 1}},
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 4}, {5, 8},
{6, 2}, {6, 4}, {6, 8}, {7, 3}, {7, 4}, {7, 8}},
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 8}, {6, 2},
{6, 8}, {7, 3}, {7, 8}, {9, 4}, {9, 5}, {9, 12},
{10, 4}, {10, 6}, {10, 12}, {11, 4}, {11, 7},
{11, 12}}, {{1, 2}, {2, 3}, {3, 1}, {5, 1}, {6, 2},
{7, 3}, {9, 4}, {9, 5}, {9, 12}, {10, 4}, {10, 6},
{10, 12}, {11, 4}, {11, 7}, {11, 12}, {13, 5},
{13, 8}, {13, 16}, {14, 6}, {14, 8}, {14, 16},
{15, 7}, {15, 8}, {15, 16}}}
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 4}, {5, 8},
{6, 2}, {6, 4}, {6, 8}, {7, 3}, {7, 4}, {7, 8}},
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 8}, {6, 2},
{6, 8}, {7, 3}, {7, 8}, {9, 4}, {9, 5}, {9, 12},
{10, 4}, {10, 6}, {10, 12}, {11, 4}, {11, 7},
{11, 12}}, {{1, 2}, {2, 3}, {3, 1}, {5, 1}, {6, 2},
{7, 3}, {9, 4}, {9, 5}, {9, 12}, {10, 4}, {10, 6},
{10, 12}, {11, 4}, {11, 7}, {11, 12}, {13, 5},
{13, 8}, {13, 16}, {14, 6}, {14, 8}, {14, 16},
{15, 7}, {15, 8}, {15, 16}}}
Length /@ %
{6, 12, 18, 24}
GraphKnobs[Last[%16]]
{{{1, 2}, {3, 2}, {4, 2}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {3, 2}, {4, 2}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {2, 3}, {3, 1}, {4, 1}, {5, 2}, {6, 3}}}
{{1, 2}, {3, 2}, {4, 2}}, {{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {2, 3}, {3, 1}, {4, 1}, {5, 2}, {6, 3}}}
Union[%]
{{{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {2, 3}, {3, 1}, {4, 1}, {5, 2}, {6, 3}}}
{{1, 2}, {2, 3}, {3, 1}, {4, 1}, {5, 2}, {6, 3}}}
GraphKnobs[tetragraph]
{{{1, 2}, {3, 2}, {4, 2}}}
Last[GraphEvolveList[knobruleA, tetragraph, 5]];
Union[GraphKnobs[%]]
{{{1, 2}, {3, 2}, {4, 2}},
{{1, 2}, {2, 3}, {3, 1}, {4, 1}, {5, 2}, {6, 3}}}
{{1, 2}, {2, 3}, {3, 1}, {4, 1}, {5, 2}, {6, 3}}}
GraphEvolveList[{knobruleB, knobruleA}, tetragraph, 4]
$Aborted
GraphEvolveList[{knobruleB, knobruleA}, tetragraph, 2]
{{{1, 4}, {1, 2}, {2, 4}, {2, 3}, {3, 4}, {3, 1}},
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 4}, {5, 8},
{6, 2}, {6, 4}, {6, 8}, {7, 3}, {7, 4}, {7, 8}},
{{2, 1}, {2, 5}, {2, 6}, {3, 1}, {3, 5}, {3, 6},
{4, 1}, {4, 5}, {4, 6}}}
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 4}, {5, 8},
{6, 2}, {6, 4}, {6, 8}, {7, 3}, {7, 4}, {7, 8}},
{{2, 1}, {2, 5}, {2, 6}, {3, 1}, {3, 5}, {3, 6},
{4, 1}, {4, 5}, {4, 6}}}
Length /@ %
{6, 12, 9}
GraphEvolveList[{knobruleB, knobruleA}, tetragraph, 3]
{{{1, 4}, {1, 2}, {2, 4}, {2, 3}, {3, 4}, {3, 1}},
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 4}, {5, 8},
{6, 2}, {6, 4}, {6, 8}, {7, 3}, {7, 4}, {7, 8}},
{{2, 1}, {2, 5}, {2, 6}, {3, 1}, {3, 5}, {3, 6},
{4, 1}, {4, 5}, {4, 6}},
{{2, 5}, {2, 6}, {3, 5}, {3, 6}, {4, 5}, {4, 6},
{7, 1}, {7, 2}, {7, 10}, {8, 1}, {8, 3}, {8, 10},
{9, 1}, {9, 4}, {9, 10}}}
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 4}, {5, 8},
{6, 2}, {6, 4}, {6, 8}, {7, 3}, {7, 4}, {7, 8}},
{{2, 1}, {2, 5}, {2, 6}, {3, 1}, {3, 5}, {3, 6},
{4, 1}, {4, 5}, {4, 6}},
{{2, 5}, {2, 6}, {3, 5}, {3, 6}, {4, 5}, {4, 6},
{7, 1}, {7, 2}, {7, 10}, {8, 1}, {8, 3}, {8, 10},
{9, 1}, {9, 4}, {9, 10}}}
Length /@ %
{6, 12, 9, 15}
Complete Graph Evolution
Complete Graph Evolution
<<NetworkSystems/NewGraphs.m
GraphStepComplete[knobruleAp, mingraphB]
{{1, 1}, {1, 2}, {2, 2}}
GraphStepComplete[knobruleAp, mingraphA]
{{3, 1}, {3, 2}, {3, 6}, {4, 1}, {4, 2}, {4, 6},
{5, 1}, {5, 2}, {5, 6}}
{5, 1}, {5, 2}, {5, 6}}
GraphEvolveCompleteList[knobruleAp, mingraphA, 2]
{{{1, 2}, {1, 2}, {1, 2}},
{{3, 1}, {3, 2}, {3, 6}, {4, 1}, {4, 2}, {4, 6},
{5, 1}, {5, 2}, {5, 6}},
{{7, 1}, {7, 3}, {7, 10}, {8, 1}, {8, 4}, {8, 10},
{9, 1}, {9, 5}, {9, 10}, {11, 2}, {11, 3}, {11, 14},
{12, 2}, {12, 4}, {12, 14}, {13, 2}, {13, 5},
{13, 14}, {15, 3}, {15, 6}, {15, 18}, {16, 4},
{16, 6}, {16, 18}, {17, 5}, {17, 6}, {17, 18}}}
{{3, 1}, {3, 2}, {3, 6}, {4, 1}, {4, 2}, {4, 6},
{5, 1}, {5, 2}, {5, 6}},
{{7, 1}, {7, 3}, {7, 10}, {8, 1}, {8, 4}, {8, 10},
{9, 1}, {9, 5}, {9, 10}, {11, 2}, {11, 3}, {11, 14},
{12, 2}, {12, 4}, {12, 14}, {13, 2}, {13, 5},
{13, 14}, {15, 3}, {15, 6}, {15, 18}, {16, 4},
{16, 6}, {16, 18}, {17, 5}, {17, 6}, {17, 18}}}
Length /@ %
{3, 9, 27}
{{{1, 4}, {1, 2}, {2, 4}, {2, 3}, {3, 4}, {3, 1}},
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 4}, {5, 8},
{6, 2}, {6, 4}, {6, 8}, {7, 3}, {7, 4}, {7, 8}},
{{2, 14}, {3, 14}, {4, 14}, {6, 1}, {6, 2}, {6, 9},
{7, 1}, {7, 3}, {7, 9}, {8, 1}, {8, 4}, {8, 9},
{10, 2}, {10, 5}, {10, 13}, {11, 3}, {11, 5},
{11, 13}, {12, 4}, {12, 5}, {12, 13}},
{{6, 2}, {7, 3}, {8, 4}, {10, 2}, {11, 3}, {12, 4},
{15, 1}, {15, 6}, {15, 18}, {16, 1}, {16, 7},
{16, 18}, {17, 1}, {17, 8}, {17, 18}, {19, 5},
{19, 10}, {19, 22}, {20, 5}, {20, 11}, {20, 22},
{21, 5}, {21, 12}, {21, 22}, {23, 6}, {23, 9},
{23, 26}, {24, 7}, {24, 9}, {24, 26}, {25, 8},
{25, 9}, {25, 26}, {27, 10}, {27, 13}, {27, 30},
{28, 11}, {28, 13}, {28, 30}, {29, 12}, {29, 13},
{29, 30}, {31, 2}, {31, 14}, {31, 34}, {32, 3},
{32, 14}, {32, 34}, {33, 4}, {33, 14}, {33, 34}}}
{{1, 2}, {2, 3}, {3, 1}, {5, 1}, {5, 4}, {5, 8},
{6, 2}, {6, 4}, {6, 8}, {7, 3}, {7, 4}, {7, 8}},
{{2, 14}, {3, 14}, {4, 14}, {6, 1}, {6, 2}, {6, 9},
{7, 1}, {7, 3}, {7, 9}, {8, 1}, {8, 4}, {8, 9},
{10, 2}, {10, 5}, {10, 13}, {11, 3}, {11, 5},
{11, 13}, {12, 4}, {12, 5}, {12, 13}},
{{6, 2}, {7, 3}, {8, 4}, {10, 2}, {11, 3}, {12, 4},
{15, 1}, {15, 6}, {15, 18}, {16, 1}, {16, 7},
{16, 18}, {17, 1}, {17, 8}, {17, 18}, {19, 5},
{19, 10}, {19, 22}, {20, 5}, {20, 11}, {20, 22},
{21, 5}, {21, 12}, {21, 22}, {23, 6}, {23, 9},
{23, 26}, {24, 7}, {24, 9}, {24, 26}, {25, 8},
{25, 9}, {25, 26}, {27, 10}, {27, 13}, {27, 30},
{28, 11}, {28, 13}, {28, 30}, {29, 12}, {29, 13},
{29, 30}, {31, 2}, {31, 14}, {31, 34}, {32, 3},
{32, 14}, {32, 34}, {33, 4}, {33, 14}, {33, 34}}}
Length /@ %
{6, 12, 21, 51}
{6, 12, 21, 51, 129, 339}
ListPlot[Log[%], PlotJoined->True] ;
{6, 12, 21, 51, 129, 339, 921}
%64/RotateRight[%64] // N
{0.00651466, 2., 1.75, 2.42857, 2.52941, 2.62791,
2.71681}
2.71681}
{6, 12, 21, 51, 129, 339, 921, 2571}
% / RotateRight[%] // N
{0.00233372, 2., 1.75, 2.42857, 2.52941, 2.62791,
2.71681, 2.79153}
2.71681, 2.79153}
ListPlot[Rest[%], PlotJoined->True] ;
{6, 12, 9, 15, 21, 27}