p5 = (x2 + x2 + x3)*(x4 + x5 + x6);
p6 = x1*x6 + x2*x5 + x3*x4;
GroebnerBasis[{p5, p6}, {x1, x2, x3, x4, x5, x6}]
{2 x2 x4 + x3 x4 + 2 x2 x5 + x3 x5 + 2 x2 x6 + x3 x6,
x3 x4 + x2 x5 + x1 x6}
where example polynomials that I would like to visualise as graphs.