Rank = 4, n = 6
Total Matrices in Space:
68719476736
Total Graphs of Consistent Rank:
67950
Total Morphs Found:
98
"Morphs" are what we call the shape of the graph, and it turns out that even though there are many thousands of graphs, when their characteristic polynomial is found, many are shared. In fact, some morphs have thousands of different graphs that produce the same morph, but each of those matrices shares the same characteristic polynomial. The characteristic polynomial and it's roots represent the "shape" of the structure, and each graph is a different permutation of numbering of the vertices.
Here are all currently identified morphs, and how many there are, with an example of each one:
There are 15 of
Partial Probability: 0%
λ6-12λ4-16λ3 = 0
There are 90 of
Partial Probability: 0%
λ6-10λ4-20λ3-16λ2 = 0
There are 40 of
Partial Probability: 0%
λ6-9λ4-20λ3-27λ2-18λ-8 = 0
There are 120 of
Partial Probability: 0%
λ6-9λ4-22λ3-21λ2-12λ = 0
There are 120 of
Partial Probability: 0%
λ6-λ5-10λ4-9λ3+λ2+10λ+8 = 0
There are 360 of
Partial Probability: 1%
λ6-λ5-10λ4-8λ3 = 0
There are 720 of
Partial Probability: 1%
λ6-λ5-8λ4-13λ3-11λ2-4λ = 0
There are 720 of
Partial Probability: 1%
λ6-λ5-9λ4-12λ3-λ2+4λ = 0
There are 90 of
Partial Probability: 0%
λ6-2λ5-10λ4+4λ3+17λ2-2λ-8 = 0
There are 180 of
Partial Probability: 0%
λ6-2λ5-10λ4+4λ3+16λ2 = 0
There are 720 of
Partial Probability: 1%
λ6-2λ5-6λ4-7λ3-4λ2 = 0
There are 1440 of
Partial Probability: 2%
λ6-2λ5-7λ4-3λ3-3λ2-4λ = 0
There are 360 of
Partial Probability: 1%
λ6-2λ5-7λ4-4λ3-λ2+4λ = 0
There are 360 of
Partial Probability: 1%
λ6-2λ5-7λ4-6λ3+5λ2+10λ+8 = 0
There are 360 of
Partial Probability: 1%
λ6-2λ5-6λ4-6λ3-5λ2-10λ-8 = 0
There are 180 of
Partial Probability: 0%
λ6-2λ5-8λ4 = 0
There are 90 of
Partial Probability: 0%
λ6-2λ5-6λ4-8λ3-3λ2+10λ+8 = 0
There are 720 of
Partial Probability: 1%
λ6-2λ5-7λ4-5λ3+4λ2 = 0
There are 720 of
Partial Probability: 1%
λ6-2λ5-8λ4-3λ3+9λ2+12λ = 0
There are 1080 of
Partial Probability: 2%
λ6-2λ5-8λ4-2λ3+7λ2+4λ = 0
There are 240 of
Partial Probability: 0%
λ6-3λ5-3λ4-λ3-9λ2-12λ = 0
There are 40 of
Partial Probability: 0%
λ6-3λ5-6λ4+7λ3+3λ2+6λ-8 = 0
There are 1440 of
Partial Probability: 2%
λ6-3λ5-4λ4+λ2-4λ = 0
There are 720 of
Partial Probability: 1%
λ6-3λ5-6λ4+6λ3+7λ2+4λ = 0
There are 240 of
Partial Probability: 0%
λ6-3λ5-3λ4-4λ3 = 0
There are 720 of
Partial Probability: 1%
λ6-3λ5-5λ4+3λ3+5λ2-2λ-8 = 0
There are 1440 of
Partial Probability: 2%
λ6-3λ5-4λ4+λ3-4λ2 = 0
There are 1440 of
Partial Probability: 2%
λ6-3λ5-6λ4+7λ3+5λ2-4λ = 0
There are 240 of
Partial Probability: 0%
λ6-3λ5-6λ4+8λ3+3λ2-12λ = 0
There are 720 of
Partial Probability: 1%
λ6-3λ5-3λ4-2λ3-7λ2-4λ = 0
There are 720 of
Partial Probability: 1%
λ6-3λ5-5λ4+λ3+11λ2+4λ = 0
There are 360 of
Partial Probability: 1%
λ6-3λ5-4λ4+λ3-5λ2+2λ+8 = 0
There are 2880 of
Partial Probability: 4%
λ6-3λ5-4λ4-λ3+3λ2+4λ = 0
There are 720 of
Partial Probability: 1%
λ6-3λ5-5λ4+2λ3+9λ2-4λ = 0
There are 360 of
Partial Probability: 1%
λ6-3λ5-6λ4+8λ3 = 0
There are 1440 of
Partial Probability: 2%
λ6-3λ5-5λ4+3λ3+4λ2 = 0
There are 360 of
Partial Probability: 1%
λ6-4λ5-4λ4+16λ3+3λ2-12λ = 0
There are 45 of
Partial Probability: 0%
λ6-4λ5-4λ4+16λ3 = 0
There are 60 of
Partial Probability: 0%
λ6-4λ5-4λ4+18λ3-5λ2-14λ+8 = 0
There are 720 of
Partial Probability: 1%
λ6-4λ5+λ4-3λ3-4λ2 = 0
There are 1800 of
Partial Probability: 3%
λ6-4λ5-λ2+4λ = 0
There are 1440 of
Partial Probability: 2%
λ6-4λ5-λ4+6λ3-7λ2-4λ = 0
There are 720 of
Partial Probability: 1%
λ6-4λ5+λ4-2λ3-9λ2+4λ = 0
There are 720 of
Partial Probability: 1%
λ6-4λ5-2λ4+6λ3+8λ2 = 0
There are 360 of
Partial Probability: 1%
λ6-4λ5-λ4+4λ3+λ2-2λ-8 = 0
There are 1440 of
Partial Probability: 2%
λ6-4λ5-λ3+4λ2 = 0
There are 360 of
Partial Probability: 1%
λ6-4λ5-2λ4+10λ3-7λ2-6λ+8 = 0
There are 2160 of
Partial Probability: 3%
λ6-4λ5-λ4+5λ3-5λ2+4λ = 0
There are 720 of
Partial Probability: 1%
λ6-4λ5-2λ4+9λ3-4λ2 = 0
There are 721 of
Partial Probability: 1%
λ6-4λ5-2λ4+7λ3+3λ2+4λ = 0
There are 1440 of
Partial Probability: 2%
λ6-4λ5-λ4+4λ3 = 0
There are 720 of
Partial Probability: 1%
λ6-4λ5-λ4+4λ3+3λ2-12λ = 0
There are 90 of
Partial Probability: 0%
λ6-4λ5-2λ4+12λ3-16λ2 = 0
There are 1440 of
Partial Probability: 2%
λ6-4λ5-2λ4+8λ3+λ2-4λ = 0
There are 360 of
Partial Probability: 1%
λ6-4λ5-λ4+2λ3+7λ2+4λ = 0
There are 2160 of
Partial Probability: 3%
λ6-4λ5+λ3-3λ2-4λ = 0
There are 360 of
Partial Probability: 1%
λ6-4λ5+λ2-6λ+8 = 0
There are 720 of
Partial Probability: 1%
λ6-4λ5-λ4+4λ3-λ2+2λ+8 = 0
There are 720 of
Partial Probability: 1%
λ6-4λ5-λ4+3λ3+5λ2-4λ = 0
There are 180 of
Partial Probability: 0%
λ6-4λ5-2λ3+7λ2+6λ-8 = 0
There are 360 of
Partial Probability: 1%
λ6-4λ5-2λ4+6λ3+9λ2-2λ-8 = 0
There are 1800 of
Partial Probability: 3%
λ6-5λ5+4λ4 = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+5λ4-5λ3+4λ2 = 0
There are 1440 of
Partial Probability: 2%
λ6-5λ5+5λ4-4λ3-λ2+4λ = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+3λ4+6λ3-9λ2+4λ = 0
There are 1440 of
Partial Probability: 2%
λ6-5λ5+3λ4+4λ3+λ2-4λ = 0
There are 360 of
Partial Probability: 1%
λ6-5λ5+4λ4+λ3-7λ2+14λ-8 = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+2λ4+9λ3-3λ2-4λ = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+3λ4+5λ3-4λ2 = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+5λ4-2λ3-8λ2 = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+5λ4-3λ3-5λ2+6λ-8 = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+4λ4-3λ2+12λ = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+2λ4+11λ3-13λ2+4λ = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+4λ4+λ3-3λ2-6λ+8 = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+4λ4+3λ3-15λ2+12λ = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+2λ4+10λ3-8λ2 = 0
There are 1440 of
Partial Probability: 2%
λ6-5λ5+4λ4+λ3-5λ2+4λ = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+6λ4-8λ3+λ2-4λ = 0
There are 2160 of
Partial Probability: 3%
λ6-5λ5+4λ4-λ3+5λ2-4λ = 0
There are 720 of
Partial Probability: 1%
λ6-5λ5+6λ4-9λ3+3λ2+4λ = 0
There are 10 of
Partial Probability: 0%
λ6-6λ5+6λ4+16λ3-39λ2+30λ-8 = 0
There are 60 of
Partial Probability: 0%
λ6-6λ5+6λ4+12λ3-15λ2-6λ+8 = 0
There are 720 of
Partial Probability: 1%
λ6-6λ5+8λ4+2λ3-9λ2+4λ = 0
There are 720 of
Partial Probability: 1%
λ6-6λ5+9λ4-3λ3-5λ2+4λ = 0
There are 120 of
Partial Probability: 0%
λ6-6λ5+9λ4-4λ3+3λ2-12λ = 0
There are 120 of
Partial Probability: 0%
λ6-6λ5+9λ4-6λ3+9λ2-6λ+8 = 0
There are 90 of
Partial Probability: 0%
λ6-6λ5+10λ4-12λ3+21λ2-22λ+8 = 0
There are 720 of
Partial Probability: 1%
λ6-6λ5+10λ4-8λ3-λ2+4λ = 0
There are 1440 of
Partial Probability: 2%
λ6-6λ5+10λ4-10λ3+9λ2-4λ = 0
There are 180 of
Partial Probability: 0%
λ6-6λ5+10λ4-8λ3-3λ2+14λ-8 = 0
There are 1200 of
Partial Probability: 2%
λ6-6λ5+9λ4-4λ3 = 0
There are 180 of
Partial Probability: 0%
λ6-6λ5+8λ4-λ2+6λ-8 = 0
There are 30 of
Partial Probability: 0%
λ6-6λ5+12λ4-16λ3 = 0
There are 240 of
Partial Probability: 0%
λ6-6λ5+12λ4-19λ3+15λ2-12λ = 0
There are 720 of
Partial Probability: 1%
λ6-6λ5+11λ4-15λ3+13λ2-4λ = 0
There are 180 of
Partial Probability: 0%
λ6-6λ5+12λ4-20λ3+19λ2-14λ+8 = 0
There are 120 of
Partial Probability: 0%
λ6-6λ5+12λ4-22λ3+27λ2-12λ = 0
There are 720 of
Partial Probability: 1%
λ6-6λ5+11λ4-14λ3+8λ2 = 0
