Python DiGraph.add_vertex方法代码示例

# 需要导入模块: from sage.graphs.all import DiGraph [as 别名]
# 或者: from sage.graphs.all.DiGraph import add_vertex [as 别名]
def _digraph_mutate( dg, k, n, m ):
    """
    Returns a digraph obtained from dg with n+m vertices by mutating at vertex k.

    INPUT:

    - ``dg`` -- a digraph with integral edge labels with ``n+m`` vertices
    - ``k`` -- the vertex at which ``dg`` is mutated

    EXAMPLES::

        sage: from sage.combinat.cluster_algebra_quiver.mutation_class import _digraph_mutate
        sage: dg = ClusterQuiver(['A',4]).digraph()
        sage: dg.edges()
        [(0, 1, (1, -1)), (2, 1, (1, -1)), (2, 3, (1, -1))]
        sage: _digraph_mutate(dg,2,4,0).edges()
        [(0, 1, (1, -1)), (1, 2, (1, -1)), (3, 2, (1, -1))]
    """
    edges = dict( ((v1,v2),label) for v1,v2,label in dg._backend.iterator_in_edges(dg,True) )
    in_edges = [ (v1,v2,edges[(v1,v2)]) for (v1,v2) in edges if v2 == k ]
    out_edges = [ (v1,v2,edges[(v1,v2)]) for (v1,v2) in edges if v1 == k ]
    in_edges_new = [ (v2,v1,(-label[1],-label[0])) for (v1,v2,label) in in_edges ]
    out_edges_new = [ (v2,v1,(-label[1],-label[0])) for (v1,v2,label) in out_edges ]
    diag_edges_new = []
    diag_edges_del = []

    for (v1,v2,label1) in in_edges:
        for (w1,w2,label2) in out_edges:
            l11,l12 = label1
            l21,l22 = label2
            if (v1,w2) in edges:
                diag_edges_del.append( (v1,w2,edges[(v1,w2)]) )
                a,b = edges[(v1,w2)]
                a,b = a+l11*l21, b-l12*l22
                diag_edges_new.append( (v1,w2,(a,b)) )
            elif (w2,v1) in edges:
                diag_edges_del.append( (w2,v1,edges[(w2,v1)]) )
                a,b = edges[(w2,v1)]
                a,b = b+l11*l21, a-l12*l22
                if a<0:
                    diag_edges_new.append( (w2,v1,(b,a)) )
                elif a>0:
                    diag_edges_new.append( (v1,w2,(a,b)) )
            else:
                a,b = l11*l21,-l12*l22
                diag_edges_new.append( (v1,w2,(a,b)) )

    del_edges = in_edges + out_edges + diag_edges_del
    new_edges = in_edges_new + out_edges_new + diag_edges_new
    new_edges += [ (v1,v2,edges[(v1,v2)]) for (v1,v2) in edges if not (v1,v2,edges[(v1,v2)]) in del_edges ]

    dg_new = DiGraph()
    for v1,v2,label in new_edges:
        dg_new._backend.add_edge(v1,v2,label,True)
    if dg_new.order() < n+m:
        dg_new_vertices = [ v for v in dg_new ]
        for i in [ v for v in dg if v not in dg_new_vertices ]:
            dg_new.add_vertex(i)

    return dg_new

# 需要导入模块: from sage.graphs.all import DiGraph [as 别名]
# 或者: from sage.graphs.all.DiGraph import add_vertex [as 别名]
def _matrix_to_digraph( M ):
    """
    Returns the digraph obtained from the matrix ``M``.
    In order to generate a quiver, we assume that ``M`` is skew-symmetrizable.

    EXAMPLES::

        sage: from sage.combinat.cluster_algebra_quiver.mutation_class import _matrix_to_digraph
        sage: _matrix_to_digraph(matrix(3,[0,1,0,-1,0,-1,0,1,0]))
        Digraph on 3 vertices
    """
    n = M.ncols()

    dg = DiGraph(sparse=True)
    for i,j in M.nonzero_positions():
        if i >= n: a,b = M[i,j],-M[i,j]
        else: a,b = M[i,j],M[j,i]
        if a > 0:
            dg._backend.add_edge(i,j,(a,b),True)
        elif i >= n:
            dg._backend.add_edge(j,i,(-a,-b),True)
    if dg.order() < M.nrows():
        for i in [ index for index in xrange(M.nrows()) if index not in dg ]:
            dg.add_vertex(i)
    return dg

# 需要导入模块: from sage.graphs.all import DiGraph [as 别名]
# 或者: from sage.graphs.all.DiGraph import add_vertex [as 别名]
    def to_dag(self):
        """
        Returns a directed acyclic graph corresponding to the skew
        partition.
        
        EXAMPLES::
        
            sage: dag = SkewPartition([[3, 2, 1], [1, 1]]).to_dag()
            sage: dag.edges()
            [('0,1', '0,2', None), ('0,1', '1,1', None)]
            sage: dag.vertices()
            ['0,1', '0,2', '1,1', '2,0']
        """
        i = 0

        #Make the skew tableau from the shape
        skew = [[1]*row_length for row_length in self.outer()]
        inner = self.inner()
        for i in range(len(inner)):
            for j in range(inner[i]):
                skew[i][j] = None

        G = DiGraph()
        for row in range(len(skew)):
            for column in range(len(skew[row])):
                if skew[row][column] is not None:
                    string = "%d,%d" % (row, column)
                    G.add_vertex(string)
                    #Check to see if there is a node to the right
                    if column != len(skew[row]) - 1:
                        newstring = "%d,%d" % (row, column+1)
                        G.add_edge(string, newstring)

                    #Check to see if there is anything below
                    if row != len(skew) - 1:
                        if len(skew[row+1]) > column:
                            if skew[row+1][column] is not None:
                                newstring = "%d,%d" % (row+1, column)
                                G.add_edge(string, newstring)
        return G

# 需要导入模块: from sage.graphs.all import DiGraph [as 别名]
# 或者: from sage.graphs.all.DiGraph import add_vertex [as 别名]
    def _digraph(self):
        r"""
        Constructs the underlying digraph and stores the result as an
        attribute.

        EXAMPLES::
        
            sage: from sage.combinat.yang_baxter_graph import SwapIncreasingOperator
            sage: ops = [SwapIncreasingOperator(i) for i in range(2)]
            sage: Y = YangBaxterGraph(root=(1,2,3), operators=ops)
            sage: Y._digraph
            Digraph on 6 vertices
        """
        digraph = DiGraph()
        digraph.add_vertex(self._root)
        queue = [self._root]
        while queue:
            u = queue.pop()
            for (v, l) in self._succesors(u):
                if v not in digraph:
                    queue.append(v)
                digraph.add_edge(u, v, l)
        return digraph