[OK] n=4: finder brute force == referee BEST/matrix-tree, all i
[OK] n=5: finder brute force == referee BEST/matrix-tree, all i
[OK] n=3: referee brute force (3 circuits = n^(n-2)((n-2)!)^n: True) == BEST/matrix-tree
[OK] n=4: referee brute force (256 circuits = n^(n-2)((n-2)!)^n: True) == BEST/matrix-tree
[OK] n=5: referee brute force (972000 circuits = n^(n-2)((n-2)!)^n: True) == BEST/matrix-tree
[OK] n=4: tree-walk DP and hazard DP (floating point) agree with the exact values, max |dev| = 0.0e+00
[OK] n=5: tree-walk DP and hazard DP (floating point) agree with the exact values, max |dev| = 7.8e-15
[OK] n=6: tree-walk DP and hazard DP (floating point) agree with the exact values, max |dev| = 1.6e-12
[OK] n=3: sum_i E N_i = n-1 and sum_i i E N_i = n(n-1) exactly
[OK] n=3: E N_2 = (n-1)/n and E N_3 = (n-1)(n^2-3n+3)/(n^2(n-2))
[OK] n=4: sum_i E N_i = n-1 and sum_i i E N_i = n(n-1) exactly
[OK] n=4: E N_2 = (n-1)/n and E N_3 = (n-1)(n^2-3n+3)/(n^2(n-2))
[OK] n=5: sum_i E N_i = n-1 and sum_i i E N_i = n(n-1) exactly
[OK] n=5: E N_2 = (n-1)/n and E N_3 = (n-1)(n^2-3n+3)/(n^2(n-2))
[OK] n=6: sum_i E N_i = n-1 and sum_i i E N_i = n(n-1) exactly
[OK] n=6: E N_2 = (n-1)/n and E N_3 = (n-1)(n^2-3n+3)/(n^2(n-2))
[OK] n=3: 3 labelled trees; E C = 2-2/n and E D_2 = 3(n-1)(n-2)/n^2
[OK] n=4: 16 labelled trees; E C = 2-2/n and E D_2 = 3(n-1)(n-2)/n^2
[OK] n=5: 125 labelled trees; E C = 2-2/n and E D_2 = 3(n-1)(n-2)/n^2
[OK] n=6: 1296 labelled trees; E C = 2-2/n and E D_2 = 3(n-1)(n-2)/n^2
[OK] n=7: 16807 labelled trees; E C = 2-2/n and E D_2 = 3(n-1)(n-2)/n^2
[OK] n=8: 262144 labelled trees; E C = 2-2/n and E D_2 = 3(n-1)(n-2)/n^2

Exact values of E N_i for n = 6 (BEST + directed matrix-tree theorem):
  i= 2  E N_i =                    5/6 = 0.833333333333
  i= 3  E N_i =                  35/48 = 0.729166666667
  i= 4  E N_i =                    5/8 = 0.625000000000
  i= 5  E N_i =             7405/13824 = 0.535662615741
  i= 6  E N_i =            37915/82944 = 0.457115644290
  i= 7  E N_i =                 55/144 = 0.381944444444
  i= 8  E N_i =          319295/995328 = 0.320793748392
  i= 9  E N_i =         780535/2985984 = 0.261399592228
  i=10  E N_i =        1923875/8957952 = 0.214767281629
  i=11  E N_i =         189275/1119744 = 0.169034172096
  i=12  E N_i =       3614995/26873856 = 0.134517167912
  i=13  E N_i =         305365/2985984 = 0.102266120649
  i=14  E N_i =         694325/8957952 = 0.077509345886
  i=15  E N_i =        746305/13436928 = 0.055541340997
  i=16  E N_i =         357755/8957952 = 0.039937141882
  i=17  E N_i =         232925/8957952 = 0.026002037073
  i=18  E N_i =         152045/8957952 = 0.016973187621
  i=19  E N_i =          43075/4478976 = 0.009617153564
  i=20  E N_i =             625/110592 = 0.005651403356
  i=21  E N_i =             625/331776 = 0.001883801119
  i=22  E N_i =             625/331776 = 0.001883801119
ALL CHECKS PASSED
