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You could do the following.

sage: k = QQ
sage: n = 10
sage: R = PolynomialRing(k, 'x', n)
sage: R
Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5, x6, x7, x8, x9 over Rational Field
sage: R.inject_variables()
Defining x0, x1, x2, x3, x4, x5, x6, x7, x8, x9
sage: verts = R.gens()
sage: edges = [(x1, x2), (x3, x7), (x4, x9)]
sage: G = Graph([verts, edges], format='vertices_and_edges')
sage: G
Graph on 10 vertices
sage: J = R.ideal([a * b for a, b in G.edges(labels=False)])
sage: J
Ideal (x4*x9, x3*x7, x1*x2) of Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5, x6, x7, x8, x9 over Rational Field