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def make_toy_graph():
    T = gt.Graph(directed = False)
    edge_weights = T.new_edge_property('double')
    T.properties[("e","weight")] = edge_weights

    T.add_vertex(n=4)

    e_1 = T.add_edge(0,1)
    e_2 = T.add_edge(1,2)
    e_3 = T.add_edge(0,0)

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def at_least_one_vertex_of_degree_above_one(graph):
    ''' check if there's at least one vertex of degree above 1 in the graph.
    '''
    graph = gt.GraphView(graph, vfilt= lambda v : v.out_degree() > 1)
    try:
        first = next(graph.vertices())
    except StopIteration:
        return False
    return True

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def total_length_graph(graph):
    v_ew, _ =vertex_degree1_edge_weight(T)
    return np.sum(v_ew.values())    
    
def response_to_iterative_pruning(graph):
    '''return the number of vertices of degree 1 as a function of the number of pruning
    '''
    response = []
    response.append((0,number_of_degree1_vertices(graph)))
    #print number_of_degree1_vertices(graph)

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