kk=ZZ
R=kk[x0,x1,x2,M]
arrows=read "number of arrows between any two vertices? "
n=value(arrows)
I=ideal(M*x0*x1*x2-(x0^n+x1^n+x2^n))
J=saturate(I,x0*x1*x2)
S=R/J
d=x0*x1*x2
D=ideal(x0*x1*x2,(x1*x2*M-x0^(n-1))*x1*x2,x0*(x0*x2*M-x1^(n-1))*x2,x0*x1*(x0*x1*M-x2^(n-1)))
m=1
D'=ideal(d^m)
M=saturate(D',D)
D'==M