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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def closed_paths(entities, vertices):
 """ Paths are lists of entity indices. We first generate vertex paths using graph cycle algorithms, and then convert them to entity paths. This will also change the ordering of entity.points in place so a path may be traversed without having to reverse the entity. Parameters entities : (n,) entity objects Entity objects vertices : (m, dimension) float Vertex points in space Returns entity_paths : sequence of (n,) int Ordered traversals of entities """

    # get a networkx graph of entities
    graph, closed = vertex_graph(entities)
    # add entities that are closed as single- entity paths
    entity_paths = np.reshape(closed, (-1, 1)).tolist()
    # look for cycles in the graph, or closed loops
    vertex_paths = np.array(nx.cycles.cycle_basis(graph))

    # loop through every vertex cycle
    for vertex_path in vertex_paths:
        # a path has no length if it has fewer than 2 vertices
        if len(vertex_path) < 2:
            continue
        # convert vertex indices to entity indices
        entity_paths.append(
            vertex_to_entity_path(vertex_path,
                                  graph,
                                  entities,
                                  vertices))
    entity_paths = np.array(entity_paths)
    return entity_paths