            raise ValueError('not a valid root edge')

    new_g = DiGraph()
    emb = graph.get_embedding()

    # finding the third outer vertex c
    emb_b = emb[b]
    idx_a = emb_b.index(a)
    c = emb_b[(idx_a + 1) % len(emb_b)]

    # initialisation
    for i in emb[c]:
        if i != a and i != b:
            new_g.add_edge((i, -3, 'red'))