Python DiGraph.allow_loops方法代码示例

# 需要导入模块: from sage.graphs.digraph import DiGraph [as 别名]
# 或者: from sage.graphs.digraph.DiGraph import allow_loops [as 别名]
    def Circuit(self,n):
        r"""
        Returns the circuit on `n` vertices

        The circuit is an oriented ``CycleGraph``

        EXAMPLE:

        A circuit is the smallest strongly connected digraph::

            sage: circuit = digraphs.Circuit(15)
            sage: len(circuit.strongly_connected_components()) == 1
            True
        """
        if n<0:
            raise ValueError("The number of vertices must be a positive integer.")

        g = DiGraph()
        g.name("Circuit on "+str(n)+" vertices")

        if n==0:
            return g
        elif n == 1:
            g.allow_loops(True)
            g.add_edge(0,0)
            return g
        else:
            g.add_edges([(i,i+1) for i in xrange(n-1)])
            g.add_edge(n-1,0)
            return g        

# 需要导入模块: from sage.graphs.digraph import DiGraph [as 别名]
# 或者: from sage.graphs.digraph.DiGraph import allow_loops [as 别名]
    def Circuit(self,n):
        r"""
        Returns the circuit on `n` vertices

        The circuit is an oriented ``CycleGraph``

        EXAMPLE:

        A circuit is the smallest strongly connected digraph::

            sage: circuit = digraphs.Circuit(15)
            sage: len(circuit.strongly_connected_components()) == 1
            True
        """
        g = DiGraph(n)
        g.name("Circuit")

        if n==0:
            return g
        elif n == 1:
            g.allow_loops(True)
            g.add_edge(0,0)
            return g
        else:
            g.add_edges([(i,i+1) for i in xrange(n-1)])
            g.add_edge(n-1,0)
            return g

# 需要导入模块: from sage.graphs.digraph import DiGraph [as 别名]
# 或者: from sage.graphs.digraph.DiGraph import allow_loops [as 别名]

#.........这里部分代码省略.........
        in the reduced Rauzy graph of order `n` whose label is the label of
        the path in `G_n`.
        
        .. NOTE::

            In the case of infinite recurrent non periodic words, this
            definition correspond to the following one that can be found in
            [1] and [2]  where a simple path is a path that begins with a
            special factor, ends with a special factor and contains no
            other vertices that are special:

            The reduced Rauzy graph of factors of length `n` is obtained
            from `G_n` by replacing each simple path `P=v_1 v_2 ...
            v_{\ell}` with an edge `v_1 v_{\ell}` whose label is the
            concatenation of the labels of the edges of `P`.

        EXAMPLES::

            sage: w = Word(range(10)); w
            word: 0123456789
            sage: g = w.reduced_rauzy_graph(3); g
            Looped multi-digraph on 2 vertices
            sage: g.vertices()
            [word: 012, word: 789]
            sage: g.edges()
            [(word: 012, word: 789, word: 3456789)]

        For the Fibonacci word::

            sage: f = words.FibonacciWord()[:100]
            sage: g = f.reduced_rauzy_graph(8);g
            Looped multi-digraph on 2 vertices
            sage: g.vertices()
            [word: 01001010, word: 01010010]
            sage: g.edges()
            [(word: 01001010, word: 01010010, word: 010), (word: 01010010, word: 01001010, word: 01010), (word: 01010010, word: 01001010, word: 10)]

        For periodic words::

            sage: from itertools import cycle
            sage: w = Word(cycle('abcd'))[:100]
            sage: g = w.reduced_rauzy_graph(3)
            sage: g.edges()
            [(word: abc, word: abc, word: dabc)]

        ::

            sage: w = Word('111')
            sage: for i in range(5) : w.reduced_rauzy_graph(i)
            Looped digraph on 1 vertex
            Looped digraph on 1 vertex
            Looped digraph on 1 vertex
            Looped multi-digraph on 1 vertex
            Looped multi-digraph on 0 vertices

        For ultimately periodic words::

            sage: sigma = WordMorphism('a->abcd,b->cd,c->cd,d->cd')
            sage: w = sigma.fixed_point('a')[:100]; w
            word: abcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcd...
            sage: g = w.reduced_rauzy_graph(5)
            sage: g.vertices()
            [word: abcdc, word: cdcdc]
            sage: g.edges()
            [(word: abcdc, word: cdcdc, word: dc), (word: cdcdc, word: cdcdc, word: dc)]

        AUTHOR:

        Julien Leroy (March 2010): initial version

        REFERENCES:

        - [1] M. Bucci et al.  A. De Luca, A. Glen, L. Q. Zamboni, A
          connection between palindromic and factor complexity using
          return words," Advances in Applied Mathematics 42 (2009) 60-74.

        - [2] L'ubomira Balkova, Edita Pelantova, and Wolfgang Steiner.
          Sequences with constant number of return words. Monatsh. Math,
          155 (2008) 251-263.
        """
        from sage.graphs.all import DiGraph
        from copy import copy
        g = copy(self.rauzy_graph(n))      
        # Otherwise it changes the rauzy_graph function.
        l = [v for v in g if g.in_degree(v)==1 and g.out_degree(v)==1]
        if g.num_verts() !=0 and len(l)==g.num_verts():       
            # In this case, the Rauzy graph is simply a cycle.
            g = DiGraph()
            g.allow_loops(True)
            g.add_vertex(self[:n])
            g.add_edge(self[:n],self[:n],self[n:n+len(l)])
        else:
            g.allow_loops(True)
            g.allow_multiple_edges(True)
            for v in l:
                [i] = g.neighbors_in(v)
                [o] = g.neighbors_out(v)
                g.add_edge(i,o,g.edge_label(i,v)[0]*g.edge_label(v,o)[0])
                g.delete_vertex(v)
        return g