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r""" 

Backends for Sage (di)graphs. 

  

This module implements :class:`GenericGraphBackend` (the base class for 

backends) and :class:`NetworkXGraphBackend` (a wrapper for `NetworkX 

<http://networkx.lanl.gov/>`__ graphs) 

  

Any graph backend must redefine the following methods (for which 

:class:`GenericGraphBackend` raises a ``NotImplementedError``) 

  

.. csv-table:: 

:class: contentstable 

:widths: 30, 70 

:delim: | 

  

:meth:`~GenericGraphBackend.add_edge` | Add an edge `(u,v)` to ``self``, with label `l`. 

:meth:`~GenericGraphBackend.add_edges` | Add a sequence of edges to ``self``. 

:meth:`~GenericGraphBackend.add_vertex` | Add a labelled vertex to ``self``. 

:meth:`~GenericGraphBackend.add_vertices` | Add labelled vertices to ``self``. 

:meth:`~GenericGraphBackend.degree` | Return the total number of vertices incident to `v`. 

:meth:`~GenericGraphBackend.in_degree` | Return the in-degree of `v` 

:meth:`~GenericGraphBackend.out_degree` | Return the out-degree of `v` 

:meth:`~GenericGraphBackend.del_edge` | Delete the edge `(u,v)` with label `l`. 

:meth:`~GenericGraphBackend.del_vertex` | Delete a labelled vertex in ``self``. 

:meth:`~GenericGraphBackend.del_vertices` | Delete labelled vertices in ``self``. 

:meth:`~GenericGraphBackend.get_edge_label` | Return the edge label of `(u,v)`. 

:meth:`~GenericGraphBackend.has_edge` | True if ``self`` has an edge `(u,v)` with label `l`. 

:meth:`~GenericGraphBackend.has_vertex` | True if ``self`` has a vertex with label `v`. 

:meth:`~GenericGraphBackend.iterator_edges` | Iterate over the edges incident to a sequence of vertices. 

:meth:`~GenericGraphBackend.iterator_in_edges` | Iterate over the incoming edges incident to a sequence of vertices. 

:meth:`~GenericGraphBackend.iterator_out_edges` | Iterate over the outbound edges incident to a sequence of vertices. 

:meth:`~GenericGraphBackend.iterator_nbrs` | Iterate over the vertices adjacent to `v`. 

:meth:`~GenericGraphBackend.iterator_in_nbrs` | Iterate over the vertices u such that the edge `(u,v)` is in ``self`` (that is, predecessors of `v`). 

:meth:`~GenericGraphBackend.iterator_out_nbrs` | Iterate over the vertices u such that the edge `(v,u)` is in ``self`` (that is, successors of `v`). 

:meth:`~GenericGraphBackend.iterator_verts` | Iterate over the vertices `v` with labels in verts. 

:meth:`~GenericGraphBackend.loops` | Get/set whether or not ``self`` allows loops. 

:meth:`~GenericGraphBackend.multiple_edges` | Get/set whether or not ``self`` allows multiple edges. 

:meth:`~GenericGraphBackend.name` | Get/set name of ``self``. 

:meth:`~GenericGraphBackend.num_edges` | The number of edges in ``self`` 

:meth:`~GenericGraphBackend.num_verts` | The number of vertices in ``self`` 

:meth:`~GenericGraphBackend.relabel` | Relabel the vertices of ``self`` by a permutation. 

:meth:`~GenericGraphBackend.set_edge_label` | Label the edge `(u,v)` by `l`. 

  

For an overview of graph data structures in sage, see 

:mod:`~sage.graphs.base.overview`. 

  

Classes and methods 

------------------- 

""" 

  

#******************************************************************************* 

# Copyright (C) 2008 Robert L. Miller <rlmillster@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#******************************************************************************* 

from __future__ import absolute_import 

  

from .c_graph cimport CGraphBackend, CGraph 

  

  

cdef class GenericGraphBackend(SageObject): 

""" 

A generic wrapper for the backend of a graph. Various graph classes use 

extensions of this class. Note, this graph has a number of placeholder 

functions, so the doctests are rather silly. 

  

TESTS:: 

  

sage: import sage.graphs.base.graph_backends 

  

""" 

_loops = False 

_multiple_edges = False 

_name = '' 

def add_edge(self, u, v, l, directed): 

""" 

Add an edge (u,v) to self, with label l. If directed is True, this is 

interpreted as an arc from u to v. 

  

INPUT: 

  

- ``u,v`` -- vertices 

- ``l`` -- edge label 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.add_edge(1,2,'a',True) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def add_edges(self, edges, directed): 

""" 

Add a sequence of edges to self. If directed is True, these are 

interpreted as arcs. 

  

INPUT: 

  

- ``edges`` -- list/iterator of edges to be added. 

  

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.add_edges([],True) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

  

def add_vertex(self, name): 

""" 

Add a labelled vertex to self. 

  

INPUT: 

  

- ``name`` -- vertex label 

  

OUTPUT: 

  

If ``name=None``, the new vertex name is returned, ``None`` otherwise. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.add_vertex(0) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def add_vertices(self, vertices): 

""" 

Add labelled vertices to self. 

  

INPUT: 

  

- ``vertices`` -- iterator of vertex labels. A new label is created, 

used and returned in the output list for all ``None`` values in 

``vertices``. 

  

OUTPUT: 

  

Generated names of new vertices if there is at least one ``None`` value 

present in ``vertices``. ``None`` otherwise. 

  

EXAMPLES:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.add_vertices([1,2,3]) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def degree(self, v, directed): 

""" 

Return the total number of vertices incident to `v`. 

  

INPUT: 

  

- ``v`` -- a vertex label 

- ``directed`` -- boolean 

  

OUTPUT: 

  

degree of v 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.degree(1, False) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def in_degree(self, v): 

r""" 

Return the in-degree of `v` 

  

INPUT: 

  

- ``v`` -- a vertex label 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.in_degree(1) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def out_degree(self, v): 

r""" 

Return the out-degree of `v` 

  

INPUT: 

  

- ``v`` -- a vertex label 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.out_degree(1) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def del_edge(self, u, v, l, directed): 

""" 

Delete the edge `(u,v)` with label `l`. 

  

INPUT: 

  

- ``u,v`` -- vertices 

- ``l`` -- edge label 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.del_edge(1,2,'a',True) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def del_vertex(self, v): 

""" 

Delete a labelled vertex in self. 

  

INPUT: 

  

- ``v`` -- vertex label 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.del_vertex(0) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def del_vertices(self, vertices): 

""" 

Delete labelled vertices in self. 

  

INPUT: 

  

- ``vertices`` -- iterator of vertex labels 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.del_vertices([1,2,3]) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def get_edge_label(self, u, v): 

""" 

Return the edge label of `(u,v)`. 

  

INPUT: 

  

- ``u,v`` -- vertex labels 

  

OUTPUT: 

  

label of `(u,v)` 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.get_edge_label(1,2) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def has_edge(self, u, v, l): 

""" 

True if self has an edge (u,v) with label l. 

  

INPUT: 

  

- ``u,v`` -- vertex labels 

- ``l`` -- label 

  

OUTPUT: 

  

boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.has_edge(1,2,'a') 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def has_vertex(self, v): 

""" 

True if self has a vertex with label v. 

  

INPUT: 

  

- ``v`` -- vertex label 

  

OUTPUT: 

boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.has_vertex(0) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def iterator_edges(self, vertices, labels): 

""" 

Iterate over the edges incident to a sequence of vertices. Edges are 

assumed to be undirected. 

  

INPUT: 

  

- ``vertices`` -- a list of vertex labels 

- ``labels`` -- boolean 

  

OUTPUT: 

  

a generator which yields edges, with or without labels 

depending on the labels parameter. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.iterator_edges([],True) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def iterator_in_edges(self, vertices, labels): 

""" 

Iterate over the incoming edges incident to a sequence of vertices. 

  

INPUT: 

  

- ``vertices`` -- a list of vertex labels 

- ``labels`` -- boolean 

  

OUTPUT: 

a generator which yields edges, with or without labels 

depending on the labels parameter. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.iterator_in_edges([],True) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def iterator_out_edges(self, vertices, labels): 

""" 

Iterate over the outbound edges incident to a sequence of vertices. 

  

INPUT: 

  

- ``vertices`` -- a list of vertex labels 

- ``labels`` -- boolean 

  

OUTPUT: 

  

a generator which yields edges, with or without labels 

depending on the labels parameter. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.iterator_out_edges([],True) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def iterator_nbrs(self, v): 

""" 

Iterate over the vertices adjacent to v. 

  

INPUT: 

  

- ``v`` -- vertex label 

  

OUTPUT: 

  

a generator which yields vertex labels 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.iterator_nbrs(0) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def iterator_in_nbrs(self, v): 

""" 

Iterate over the vertices u such that the edge (u,v) is in self 

(that is, predecessors of v). 

  

INPUT: 

  

- ``v`` -- vertex label 

  

OUTPUT: 

  

a generator which yields vertex labels 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.iterator_in_nbrs(0) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def iterator_out_nbrs(self, v): 

""" 

Iterate over the vertices u such that the edge (v,u) is in self 

(that is, successors of v). 

  

INPUT: 

  

- ``v`` -- vertex label 

  

OUTPUT: 

  

a generator which yields vertex labels 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.iterator_out_nbrs(0) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def iterator_verts(self, verts): 

""" 

Iterate over the vertices v with labels in verts. 

  

INPUT: 

  

- ``vertex`` -- vertex labels 

  

OUTPUT: 

  

a generator which yields vertices 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.iterator_verts(0) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

  

def loops(self, new=None): 

""" 

Get/set whether or not self allows loops. 

  

INPUT: 

  

- ``new`` -- can be a boolean (in which case it sets the value) or 

``None``, in which case the current value is returned. It is set to 

``None`` by default. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.loops(True) 

Traceback (most recent call last): 

... 

NotImplementedError 

sage: G.loops(None) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def multiple_edges(self, new=None): 

""" 

Get/set whether or not self allows multiple edges. 

  

INPUT: 

  

- ``new`` -- can be a boolean (in which case it sets the value) or 

``None``, in which case the current value is returned. It is set to 

``None`` by default. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.multiple_edges(True) 

Traceback (most recent call last): 

... 

NotImplementedError 

sage: G.multiple_edges(None) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def name(self, new=None): 

""" 

Get/set name of self. 

  

INPUT: 

  

- ``new`` -- can be a string (in which case it sets the value) or 

``None``, in which case the current value is returned. It is set to 

``None`` by default. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.name("A Generic Graph") 

Traceback (most recent call last): 

... 

NotImplementedError 

sage: G.name(None) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def num_edges(self, directed): 

""" 

The number of edges in self 

  

INPUT: 

  

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.num_edges(True) 

Traceback (most recent call last): 

... 

NotImplementedError 

sage: G.num_edges(False) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def num_verts(self): 

""" 

The number of vertices in self 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.num_verts() 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def relabel(self, perm, directed): 

""" 

Relabel the vertices of self by a permutation. 

  

INPUT: 

  

- ``perm`` -- permutation 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.relabel([],False) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

def set_edge_label(self, u, v, l, directed): 

""" 

Label the edge (u,v) by l. 

  

INPUT: 

  

- ``u,v`` -- vertices 

- ``l`` -- edge label 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.GenericGraphBackend() 

sage: G.set_edge_label(1,2,'a',True) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError() 

  

def __reduce__(self): 

r"""" 

Return a tuple used for pickling this graph. 

  

This function returns a pair ``(f, args)`` such that ``f(*args)`` 

produces a copy of ``self``. The function returned is always 

:func:`unpickle_graph_backend`. 

  

Pickling of the static graph backend makes pickling of immutable 

graphs and digraphs work:: 

  

sage: G = Graph(graphs.PetersenGraph(), immutable=True) 

sage: G == loads(dumps(G)) 

True 

sage: uc = [[2,3], [], [1], [1], [1], [3,4]] 

sage: D = DiGraph(dict([[i,uc[i]] for i in range(len(uc))]), immutable=True) 

sage: loads(dumps(D)) == D 

True 

  

No problems with loops and multiple edges, with Labels:: 

  

sage: g = Graph(multiedges = True, loops = True) 

sage: g.add_edges(2*graphs.PetersenGraph().edges()) 

sage: g.add_edge(0,0) 

sage: g.add_edge(1,1, "a label") 

sage: g.add_edge([(0,1,"labellll"), (0,1,"labellll"), (0,1,"LABELLLL")]) 

sage: g.add_vertex("isolated vertex") 

sage: gi = g.copy(immutable=True) 

sage: loads(dumps(gi)) == gi 

True 

  

Similar, with a directed graph:: 

  

sage: g = DiGraph(multiedges = True, loops = True) 

sage: H = 2*(digraphs.Circuit(15)+DiGraph(graphs.PetersenGraph())) 

sage: g.add_edges(H.edges()) 

sage: g.add_edge(0,0) 

sage: g.add_edge(1,1, "a label") 

sage: g.add_edge([(0,1,"labellll"), (0,1,"labellll"), (0,1,"LABELLLL")]) 

sage: g.add_vertex("isolated vertex") 

sage: gi = g.copy(immutable=True) 

sage: loads(dumps(gi)) == gi 

True 

""" 

from .static_sparse_backend import StaticSparseBackend 

from .sparse_graph import SparseGraphBackend 

from .dense_graph import DenseGraphBackend 

  

# implementation, data_structure, multiedges, directed, loops 

if isinstance(self, CGraphBackend): 

implementation = "c_graph" 

if isinstance(self,SparseGraphBackend): 

data_structure = "sparse" 

elif isinstance(self,DenseGraphBackend): 

data_structure = "dense" 

elif isinstance(self,StaticSparseBackend): 

implementation = "static_sparse" 

else: 

raise Exception 

multiedges = (<CGraphBackend> self)._multiple_edges 

directed = (<CGraphBackend> self)._directed 

loops = (<CGraphBackend> self)._loops 

elif isinstance(self, NetworkXGraphBackend): 

data_structure = "implementation" 

implementation = "networkx" 

multiedges = self._nxg.is_multigraph() 

directed = self._nxg.is_directed() 

loops = bool(self._nxg.number_of_selfloops) 

else: 

raise Exception 

  

# Vertices and edges 

vertices = list(self.iterator_verts(None)) 

if directed: 

edges = list(self.iterator_out_edges(vertices,True)) 

else: 

edges = list(self.iterator_edges(vertices,True)) 

  

return (unpickle_graph_backend, 

(directed, vertices, edges, 

{'loops': loops, 

'multiedges': multiedges})) 

  

def unpickle_graph_backend(directed,vertices,edges,kwds): 

r""" 

Return a backend from its pickled data 

  

This methods is defined because Python's pickling mechanism can only build 

objects from a pair ``(f,args)`` by running ``f(*args)``. In particular, 

there is apparently no way to define a ``**kwargs`` (i.e. define the value 

of keyword arguments of ``f``), which means that one must know the order of 

all arguments of ``f`` (here, ``f`` is :class:`Graph` or :class:`DiGraph`). 

  

As a consequence, this means that the order cannot change in the future, 

which is something we cannot swear. 

  

INPUT: 

  

- ``directed`` (boolean) 

  

- ``vertices`` -- list of vertices. 

  

- ``edges`` -- list of edges 

  

- ``kwds`` -- any dictionary whose keywords will be forwarded to the graph 

constructor. 

  

This function builds a :class:`Graph` or :class:`DiGraph` from its data, and 

returns the ``_backend`` attribute of this object. 

  

EXAMPLES:: 

  

sage: from sage.graphs.base.graph_backends import unpickle_graph_backend 

sage: b = unpickle_graph_backend(0,[0,1,2,3],[(0,3,'label'),(0,0,1)],{'loops':True}) 

sage: b 

<sage.graphs.base.sparse_graph.SparseGraphBackend object at ...> 

sage: list(b.iterator_edges(range(4),1)) 

[(0, 0, 1), (0, 3, 'label')] 

""" 

if directed: 

from sage.graphs.digraph import DiGraph as constructor 

else: 

from sage.graphs.graph import Graph as constructor 

  

G = constructor(data=edges,**kwds) 

G.add_vertices(vertices) 

return G._backend 

  

class NetworkXGraphDeprecated(SageObject): 

""" 

Class for unpickling old networkx.XGraph formats 

  

TESTS:: 

  

sage: from sage.graphs.base.graph_backends import NetworkXGraphDeprecated as NXGD 

sage: X = NXGD() 

doctest:... 

  

""" 

  

def __init__(self): 

""" 

Issue deprecation warnings for the old networkx XGraph formats 

  

EXAMPLES:: 

  

sage: from sage.graphs.base.graph_backends import NetworkXGraphDeprecated 

sage: NetworkXGraphDeprecated() 

<sage.graphs.base.graph_backends.NetworkXGraphDeprecated object at ...> 

""" 

from sage.misc.superseded import deprecation 

deprecation(10900, "Your graph object is saved in an old format since networkx "+ 

"was updated to 1.0.1. You can re-save your graph by typing "+ 

"graph.save(filename) to make this warning go away.") 

  

def mutate(self): 

""" 

Change the old networkx XGraph format into the new one. 

  

OUTPUT: 

  

- The networkx.Graph or networkx.MultiGraph corresponding to the 

unpickled data. 

  

EXAMPLES:: 

  

sage: from sage.graphs.base.graph_backends import NetworkXGraphDeprecated as NXGD 

sage: X = NXGD() 

sage: X.adj = {1:{2:7}, 2:{1:7}, 3:{2:[4,5,6,7]}, 2:{3:[4,5,6,7]}} 

sage: X.multiedges = True 

sage: G = X.mutate() 

sage: G.edges() 

[(1, 2), (2, 3)] 

sage: G.edges(data=True) 

[(1, 2, {'weight': 7}), (2, 3, {4: {}, 5: {}, 6: {}, 7: {}})] 

  

""" 

import networkx 

new_adj = {} 

  

for node1, edges in self.adj.iteritems(): 

new_adj[node1] = {} 

for node2, weights in edges.iteritems(): 

new_adj[node1][node2] = {} 

if weights is not None: 

try: 

for weight in weights: 

new_adj[node1][node2][weight] = {} 

except TypeError: 

new_adj[node1][node2]['weight'] = weights 

  

if self.multiedges: 

G = networkx.MultiGraph(new_adj) 

else: 

G = networkx.Graph(new_adj) 

  

return G 

  

class NetworkXDiGraphDeprecated(SageObject): 

""" 

Class for unpickling old networkx.XDiGraph formats 

  

TESTS:: 

  

sage: import sage.graphs.base.graph_backends 

""" 

  

def __init__(self): 

""" 

Issue deprecation warnings for the old networkx XDiGraph formats 

  

EXAMPLES:: 

  

sage: from sage.graphs.base.graph_backends import NetworkXDiGraphDeprecated 

sage: NetworkXDiGraphDeprecated() 

doctest:... 

<sage.graphs.base.graph_backends.NetworkXDiGraphDeprecated object at ...> 

""" 

from sage.misc.superseded import deprecation 

deprecation(10900, "Your digraph object is saved in an old format since networkx "+ 

"was updated to 1.0.1. You can re-save your digraph by typing "+ 

"digraph.save(filename) to make this warning go away.") 

  

def mutate(self): 

""" 

Change the old networkx XDiGraph format into the new one. 

  

OUTPUT: 

  

- The networkx.DiGraph or networkx.MultiDiGraph corresponding to the 

unpickled data. 

  

EXAMPLES:: 

  

sage: from sage.graphs.base.graph_backends import NetworkXDiGraphDeprecated as NXDGD 

sage: X = NXDGD() 

sage: X.adj = {1:{2:7}, 2:{1:[7,8], 3:[4,5,6,7]}} 

sage: X.multiedges = True 

sage: G = X.mutate() 

sage: G.edges() 

[(1, 2), (2, 1), (2, 3)] 

sage: G.edges(data=True) 

[(1, 2, {'weight': 7}), 

(2, 1, {7: {}, 8: {}}), 

(2, 3, {4: {}, 5: {}, 6: {}, 7: {}})] 

  

""" 

import networkx 

new_adj = {} 

  

for node1, edges in self.adj.iteritems(): 

new_adj[node1] = {} 

for node2, weights in edges.iteritems(): 

new_adj[node1][node2] = {} 

if weights is not None: 

try: 

for weight in weights: 

new_adj[node1][node2][weight] = {} 

except TypeError: 

new_adj[node1][node2]['weight'] = weights 

  

if self.multiedges: 

G = networkx.MultiDiGraph(new_adj) 

else: 

G = networkx.DiGraph(new_adj) 

  

return G 

  

from sage.structure.sage_object import register_unpickle_override 

register_unpickle_override('networkx.xgraph','XGraph', NetworkXGraphDeprecated) 

register_unpickle_override('networkx.xdigraph','XDiGraph', NetworkXDiGraphDeprecated) 

  

class NetworkXGraphBackend(GenericGraphBackend): 

""" 

A wrapper for NetworkX as the backend of a graph. 

  

TESTS:: 

  

sage: import sage.graphs.base.graph_backends 

  

""" 

  

_nxg = None 

  

def __init__(self, N=None): 

""" 

Initialize the backend with NetworkX graph N. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

doctest:...: DeprecationWarning: This class is not supported anymore and will soon be removed 

See http://trac.sagemath.org/18375 for details. 

sage: G.iterator_edges([],True) 

<generator object at ...> 

""" 

if N is None: 

import networkx 

N = networkx.MultiGraph() 

self._nxg = N 

from sage.misc.superseded import deprecation 

deprecation(18375,"This class is not supported anymore and will " 

"soon be removed") 

  

def __setstate__(self,state): 

r""" 

Fix the deprecated class if necessary. 

""" 

for k,v in state.iteritems(): 

self.__dict__[k] = v 

if isinstance(self._nxg, (NetworkXGraphDeprecated, NetworkXDiGraphDeprecated)): 

from sage.misc.superseded import deprecation 

deprecation(18375,"You unpickled an object which relies on an old " 

"data structure. Save it again to update it, for it " 

"may break in the future.") 

self._nxg = self._nxg.mutate() 

  

def add_edge(self, u, v, l, directed): 

""" 

Add an edge (u,v) to self, with label l. If directed is True, this is 

interpreted as an arc from u to v. 

  

INPUT: 

  

- ``u,v`` -- vertices 

- ``l`` -- edge label 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.add_edge(1,2,'a',True) 

""" 

  

if u is None: u = self.add_vertex(None) 

if v is None: v = self.add_vertex(None) 

  

if l: 

self._nxg.add_edge(u, v, weight=l) 

else: 

self._nxg.add_edge(u, v) 

  

def add_edges(self, edges, directed): 

""" 

Add a sequence of edges to self. If directed is True, these are 

interpreted as arcs. 

  

INPUT: 

  

- ``edges`` -- list/iterator of edges to be added. 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.add_edges([],True) 

""" 

for e in edges: 

try: 

u,v,l = e 

except ValueError: 

u,v = e 

l = None 

self.add_edge(u,v,l,directed) 

  

def add_vertex(self, name): 

""" 

Add a labelled vertex to self. 

  

INPUT: 

  

- ``name``: vertex label 

  

OUTPUT: 

  

If ``name=None``, the new vertex name is returned. ``None`` otherwise. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.add_vertex(0) 

""" 

if isinstance(self._nxg, (NetworkXGraphDeprecated, NetworkXDiGraphDeprecated)): 

self._nxg = self._nxg.mutate() 

  

retval = None 

if name is None: # then find an integer to use as a key 

i = 0 

while self.has_vertex(i): 

i=i+1 

name = i 

retval = name 

  

self._nxg.add_node(name) 

  

return retval 

  

def add_vertices(self, vertices): 

""" 

Add labelled vertices to self. 

  

INPUT: 

  

- ``vertices``: iterator of vertex labels. A new label is created, used and returned in 

the output list for all ``None`` values in ``vertices``. 

  

OUTPUT: 

  

Generated names of new vertices if there is at least one ``None`` value 

present in ``vertices``. ``None`` otherwise. 

  

EXAMPLES:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.add_vertices([1,2,3]) 

sage: G.add_vertices([4,None,None,5]) 

[0, 6] 

""" 

vertices = list(vertices) 

nones = vertices.count(None) 

vertices = [v for v in vertices if v is not None] 

self._nxg.add_nodes_from(vertices) 

  

new_names = [] 

i = 0 

while nones > 0: 

while self.has_vertex(i): 

i += 1 

self._nxg.add_node(i) 

new_names.append(i) 

  

nones -= 1 

i += 1 

  

return new_names if new_names != [] else None 

  

def degree(self, v, directed): 

""" 

Return the total number of vertices incident to `v`. 

  

INPUT: 

  

- ``v`` -- a vertex label 

- ``directed`` -- boolean 

  

OUTPUT: 

  

degree of v 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.add_vertices(range(3)) 

sage: G.degree(1, False) 

0 

""" 

return self._nxg.degree(v) 

  

def in_degree(self, v): 

""" 

Return the in-degree of `v`. 

  

INPUT: 

  

- ``v`` -- a vertex label 

  

OUTPUT: 

  

degree of v 

  

TESTS:: 

  

sage: G = DiGraph(digraphs.Path(5),implementation="networkx") 

doctest:...: DeprecationWarning: The 'implementation' keyword is deprecated, and the graphs has been stored as a 'c_graph' 

See http://trac.sagemath.org/18375 for details. 

sage: G = G._backend 

sage: G.in_degree(0) 

0 

sage: G.in_degree(4) 

1 

""" 

return self._nxg.in_degree(v) 

  

def out_degree(self, v): 

""" 

Return the out-degree of `v`. 

  

INPUT: 

  

- ``v`` -- a vertex label 

  

OUTPUT: 

  

degree of v 

  

TESTS:: 

  

sage: G = DiGraph(digraphs.Path(5),implementation="networkx") 

doctest:...: DeprecationWarning: The 'implementation' keyword is deprecated, and the graphs has been stored as a 'c_graph' 

See http://trac.sagemath.org/18375 for details. 

sage: G = G._backend 

sage: G.out_degree(0) 

1 

sage: G.out_degree(4) 

0 

""" 

return self._nxg.out_degree(v) 

  

def del_edge(self, u, v, l, directed): 

""" 

Delete the edge `(u,v)` with label `l`. 

  

INPUT: 

  

- ``u,v`` -- vertices 

- ``l`` -- edge label 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.del_edge(1,2,'a',True) 

""" 

import networkx 

try: 

if self._nxg.is_multigraph(): 

for k,d in self._nxg.edge[u][v].iteritems(): 

if d.get('weight',None) == l: 

self._nxg.remove_edge(u,v,k) 

break 

else: 

if l is None or self._nxg.edge[u][v].get('weight',None) == l: 

self._nxg.remove_edge(u,v) 

except (KeyError, networkx.NetworkXError): 

pass 

  

  

def del_vertex(self, v): 

""" 

Delete a labelled vertex in self. 

  

INPUT: 

  

- ``v`` -- vertex label 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.del_vertex(0) 

Traceback (most recent call last): 

... 

NetworkXError: The node 0 is not in the graph. 

""" 

self._nxg.remove_node(v) 

  

def del_vertices(self, vertices): 

""" 

Delete labelled vertices in self. 

  

INPUT: 

  

- ``vertices`` -- iterator of vertex labels 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.del_vertices([1,2,3]) 

Traceback (most recent call last): 

... 

NetworkXError: The node 1 is not in the graph. 

""" 

for v in vertices: 

self._nxg.remove_node(v) 

  

def get_edge_label(self, u, v): 

""" 

Return the edge label of `(u,v)`. 

  

INPUT: 

  

- ``u,v`` -- vertex labels 

  

OUTPUT: 

label of `(u,v)` 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.get_edge_label(1,2) 

Traceback (most recent call last): 

... 

NetworkXError: Edge (1,2) requested via get_edge_label does not exist. 

""" 

cdef dict E 

try: 

E = self._nxg.edge[u][v] 

except KeyError: 

from networkx import NetworkXError 

raise NetworkXError("Edge (%s,%s) requested via get_edge_label does not exist."%(u,v)) 

  

if self._nxg.is_multigraph(): 

return [ e.get('weight',None) for e in E.itervalues() ] 

else: 

return E.get('weight',None) 

  

def has_edge(self, u, v, l): 

""" 

True if self has an edge (u,v) with label l. 

  

INPUT: 

  

- ``u,v`` -- vertex labels 

- ``l`` -- label 

  

OUTPUT: 

boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.has_edge(1,2,'a') 

False 

""" 

if not self._nxg.has_edge(u, v): 

return False 

if l is None: 

return True 

cdef dict E = self._nxg.adj[u][v] 

if self._nxg.is_multigraph(): 

return any(e.get('weight', None) == l 

for e in E.itervalues()) 

else: 

return any(e == l for e in E.itervalues()) 

  

def has_vertex(self, v): 

""" 

True if self has a vertex with label v. 

  

INPUT: 

  

- ``v`` -- vertex label 

  

OUTPUT: 

boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.has_vertex(0) 

False 

""" 

return self._nxg.has_node(v) 

  

def iterator_edges(self, vertices, labels): 

""" 

Iterate over the edges incident to a sequence of vertices. Edges are 

assumed to be undirected. 

  

INPUT: 

  

- ``vertices`` -- a list of vertex labels 

- ``labels`` -- boolean 

  

OUTPUT: 

a generator which yields edges, with or without labels 

depending on the labels parameter. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.iterator_edges([],True) 

<generator object at ...> 

""" 

if labels: 

for u,v,d in self._nxg.edges_iter(data=True): 

if u in vertices or v in vertices: 

yield (u,v,d.get('weight',None)) 

else: 

for u,v in self._nxg.edges_iter(): 

if u in vertices or v in vertices: 

yield (u,v) 

  

def _iterator_in_edges_with_labels(self, vertices): 

""" 

Iterate over the incoming edges incident to a sequence of vertices. 

Special case, only for internal use. 

  

EXAMPLES:: 

  

sage: g = DiGraph(graphs.PetersenGraph(), implementation="networkx")._backend 

doctest:...: DeprecationWarning: The 'implementation' keyword is deprecated, and the graphs has been stored as a 'c_graph' 

See http://trac.sagemath.org/18375 for details. 

sage: sorted(list(g.iterator_in_edges([0,1], True))) 

[(0, 1, None), (1, 0, None), (2, 1, None), (4, 0, None), (5, 0, None), (6, 1, None)] 

""" 

for u,v,d in self._nxg.in_edges_iter(vertices,data=True): 

yield (u,v,d.get('weight',None)) 

  

def iterator_in_edges(self, vertices, labels): 

""" 

Iterate over the incoming edges incident to a sequence of vertices. 

  

INPUT: 

  

- ``vertices`` -- a list of vertex labels 

- ``labels`` -- boolean 

  

OUTPUT: 

a generator which yields edges, with or without labels 

depending on the labels parameter. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: i = G.iterator_in_edges([],True) 

""" 

if self._nxg.is_directed(): 

if labels: 

return self._iterator_in_edges_with_labels(vertices) 

else: 

return self._nxg.in_edges_iter(vertices) 

else: 

return self.iterator_edges(vertices,labels) 

  

def _iterator_out_edges_with_labels(self, vertices): 

""" 

Iterate over the outbound edges incident to a sequence of vertices. 

Special case, only for internal use. 

  

EXAMPLES:: 

  

sage: g = DiGraph(graphs.PetersenGraph(), implementation="networkx")._backend 

doctest:...: DeprecationWarning: The 'implementation' keyword is deprecated, and the graphs has been stored as a 'c_graph' 

See http://trac.sagemath.org/18375 for details. 

sage: sorted(list(g.iterator_out_edges([0,1], True))) 

[(0, 1, None), (0, 4, None), (0, 5, None), (1, 0, None), (1, 2, None), (1, 6, None)] 

""" 

for u,v,d in self._nxg.out_edges_iter(vertices,data=True): 

yield (u,v,d.get('weight',None)) 

  

def iterator_out_edges(self, vertices, labels): 

""" 

Iterate over the outbound edges incident to a sequence of vertices. 

  

INPUT: 

  

- ``vertices`` -- a list of vertex labels 

- ``labels`` -- boolean 

  

OUTPUT: 

a generator which yields edges, with or without labels 

depending on the labels parameter. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: i = G.iterator_out_edges([],True) 

""" 

if self._nxg.is_directed(): 

if labels: 

return self._iterator_out_edges_with_labels(vertices) 

else: 

return self._nxg.out_edges_iter(vertices) 

else: 

return self.iterator_edges(vertices,labels) 

  

def iterator_nbrs(self, v): 

""" 

Iterate over the vertices adjacent to v. 

  

INPUT: 

  

- ``v`` -- vertex label 

  

OUTPUT: 

a generator which yields vertex labels 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.add_vertex(0) 

sage: G.iterator_nbrs(0) 

<dictionary-keyiterator object at ...> 

""" 

return self._nxg.neighbors_iter(v) 

  

def iterator_in_nbrs(self, v): 

""" 

Iterate over the vertices u such that the edge (u,v) is in self 

(that is, predecessors of v). 

  

INPUT: 

  

- ``v`` -- vertex label 

  

OUTPUT: 

a generator which yields vertex labels 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.iterator_in_nbrs(0) 

Traceback (most recent call last): 

... 

AttributeError: 'MultiGraph' object has no attribute 'predecessors_iter' 

""" 

return self._nxg.predecessors_iter(v) 

  

def iterator_out_nbrs(self, v): 

""" 

Iterate over the vertices u such that the edge (v,u) is in self 

(that is, successors of v). 

  

INPUT: 

  

- ``v`` -- vertex label 

  

OUTPUT: 

a generator which yields vertex labels 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.iterator_out_nbrs(0) 

Traceback (most recent call last): 

... 

AttributeError: 'MultiGraph' object has no attribute 'successors_iter' 

""" 

return self._nxg.successors_iter(v) 

  

def iterator_verts(self, verts): 

""" 

Iterate over the vertices v with labels in verts. 

  

INPUT: 

  

- ``vertex`` -- vertex labels 

  

OUTPUT: 

a generator which yields vertices 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.iterator_verts(0) 

<generator object bunch_iter at ...> 

""" 

return self._nxg.nbunch_iter(verts) 

  

def loops(self, new=None): 

""" 

Get/set whether or not self allows loops. 

  

INPUT: 

  

- ``new`` -- can be a boolean (in which case it sets the value) or 

``None``, in which case the current value is returned. It is set to 

``None`` by default. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.loops(True) 

sage: G.loops(None) 

True 

""" 

if new is None: 

return self._loops 

if new: 

self._loops = True 

else: 

self._loops = False 

  

def multiple_edges(self, new=None): 

""" 

Get/set whether or not self allows multiple edges. 

  

INPUT: 

  

- ``new`` -- can be a boolean (in which case it sets the value) or 

``None``, in which case the current value is returned. It is set to 

``None`` by default. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.multiple_edges(True) 

sage: G.multiple_edges(None) 

True 

""" 

from networkx import Graph,MultiGraph,DiGraph,MultiDiGraph 

if new is None: 

return self._nxg.is_multigraph() 

if new == self._nxg.is_multigraph(): 

return 

if new: 

if self._nxg.is_directed(): 

self._nxg = MultiDiGraph(self._nxg) 

else: 

self._nxg = MultiGraph(self._nxg) 

else: 

if self._nxg.is_directed(): 

self._nxg = DiGraph(self._nxg) 

else: 

self._nxg = Graph(self._nxg) 

  

def name(self, new=None): 

""" 

Get/set name of self. 

  

INPUT: 

  

- ``new`` -- can be a string (in which case it sets the value) or 

``None``, in which case the current value is returned. It is set to 

``None`` by default. 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.name("A NetworkX Graph") 

sage: G.name(None) 

'A NetworkX Graph' 

""" 

if new is None: 

return self._nxg.name 

self._nxg.name = new 

  

def num_edges(self, directed): 

""" 

The number of edges in self 

  

INPUT: 

  

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.num_edges(True) 

0 

sage: G.num_edges(False) 

0 

""" 

return self._nxg.size() 

  

def num_verts(self): 

""" 

The number of vertices in self 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.num_verts() 

0 

""" 

return self._nxg.order() 

  

def relabel(self, perm, directed): 

""" 

Relabel the vertices of self by a permutation. 

  

INPUT: 

  

- ``perm`` -- permutation 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.relabel([],False) 

""" 

from networkx import relabel_nodes 

name = self._nxg.name 

self._nxg = relabel_nodes(self._nxg,perm) 

self._nxg.name = name 

  

def set_edge_label(self, u, v, l, directed): 

""" 

Label the edge (u,v) by l. 

  

INPUT: 

  

- ``u,v`` -- vertices 

- ``l`` -- edge label 

- ``directed`` -- boolean 

  

TESTS:: 

  

sage: G = sage.graphs.base.graph_backends.NetworkXGraphBackend() 

sage: G.set_edge_label(1,2,'a',True) 

""" 

if not self.has_edge(u, v, None): 

return 

if self.multiple_edges(None): 

self._nxg[u][v].clear() 

self._nxg[u][v][0] = dict(weight=l) 

if directed is False: 

self._nxg[v][u].clear() 

self._nxg[v][u][0] = dict(weight=l) 

else: 

self._nxg[u][v]['weight'] = l 

if directed is False: 

self._nxg[v][u]['weight'] = l