複雑な条件でグラフセットを作成するにはgraphillion.graphset.graphsを使えば良さそう。 graphillion.graphset.graphsで指定できる引数は以下の通り: graphillion/ at master · takemaru/graphillion · GitHub

graphs(vertex_groups=None, degree_constraints=None, num_edges=None, no_loop=False, graphset=None, linear_constraints=None)
    Returns a GraphSet with graphs under given constraints.
    This is the base method for specific graph classes, e.g.,
    paths and trees.
    This method can be parallelized with OpenMP by specifying the
    environmental variable `OMP_NUM_THREADS`:
      `$ OMP_NUM_THREADS=4 python`
      vertex_groups: Optional.  A nested list.  Vertices in an
        inner list are connected while those in different inner
        lists are disconnected.  For `[[1, 5], [3]]`, 1 and 5 are
        connected, while they are not connected with 3.
      degree_constraints: Optional.  A dict with a vertex and a
        range or int.  The degree of a vertex is restricted by the
        range.  For `{1: 2, 6: range(2)}`, the degree of vertex 1
        is 2 and that of 6 is less than 2, while others are not
      num_edges: Optional.  A range or int.  This argument
        specifies the number of edges used in graphs to be stored.
        For `range(5)`, less than 5 edges can be used.
      no_loop: Optional.  True or False.  This argument specifies
        if loop is not allowed.
      graphset: Optional.  A GraphSet object.  Graphs to be stored
        are selected from this object.
      linear_constraints: Optional.  A list of linear constraints.
        A linear constraint consists of weighted edges and
        lower/upper bounds.  An edge weight is a positive or
        negative number, which defaults to 1.  Weights of the edges
        that are not included in the constraint are zeros.  For
        instance, `linear_constraints=[([(1, 2, 0.6), (2, 5),
        (3, 6, 1.2)], (1.5, 2.0))]`, feasible graph weights are
        between 1.5 and 2.0, e.g., `[(1, 2), (2, 3), (3, 6)]` or
        `[(1, 2), (2, 5), (5, 6)]`.
        See graphillion/test/ in detail.
      A new GraphSet object.

vertex_groups, degree_constraints, no_loopはdocstringに書いてある通りの意味。


graphsetにGraphSet オブジェクトを指定するとユニバースではなくこのgraphsetからグラフが列挙される(?)

linear_constraintsは $$ l \leq \sum_{e \in E} w_e \leq u $$ の形の線形制約を複数与えることができる。