"""Base class for MultiGraph."""
# Copyright (C) 2004-2016 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
from copy import deepcopy
import networkx as nx
from networkx.classes.graph import Graph
from networkx import NetworkXError
__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Dan Schult(dschult@colgate.edu)'])
[docs]class MultiGraph(Graph):
"""
An undirected graph class that can store multiedges.
Multiedges are multiple edges between two nodes. Each edge
can hold optional data or attributes.
A MultiGraph holds undirected edges. Self loops are allowed.
Nodes can be arbitrary (hashable) Python objects with optional
key/value attributes.
Edges are represented as links between nodes with optional
key/value attributes.
Parameters
----------
data : input graph
Data to initialize graph. If data=None (default) an empty
graph is created. The data can be any format that is supported
by the to_networkx_graph() function, currently including edge list,
dict of dicts, dict of lists, NetworkX graph, NumPy matrix
or 2d ndarray, SciPy sparse matrix, or PyGraphviz graph.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to graph as key=value pairs.
See Also
--------
Graph
DiGraph
MultiDiGraph
Examples
--------
Create an empty graph structure (a "null graph") with no nodes and
no edges.
>>> G = nx.MultiGraph()
G can be grown in several ways.
**Nodes:**
Add one node at a time:
>>> G.add_node(1)
Add the nodes from any container (a list, dict, set or
even the lines from a file or the nodes from another graph).
>>> G.add_nodes_from([2,3])
>>> G.add_nodes_from(range(100,110))
>>> H=nx.path_graph(10)
>>> G.add_nodes_from(H)
In addition to strings and integers any hashable Python object
(except None) can represent a node, e.g. a customized node object,
or even another Graph.
>>> G.add_node(H)
**Edges:**
G can also be grown by adding edges.
Add one edge,
>>> key = G.add_edge(1, 2)
a list of edges,
>>> keys = G.add_edges_from([(1,2),(1,3)])
or a collection of edges,
>>> keys = G.add_edges_from(list(H.edges()))
If some edges connect nodes not yet in the graph, the nodes
are added automatically. If an edge already exists, an additional
edge is created and stored using a key to identify the edge.
By default the key is the lowest unused integer.
>>> keys = G.add_edges_from([(4,5,dict(route=282)), (4,5,dict(route=37))])
>>> G[4]
{3: {0: {}}, 5: {0: {}, 1: {'route': 282}, 2: {'route': 37}}}
**Attributes:**
Each graph, node, and edge can hold key/value attribute pairs
in an associated attribute dictionary (the keys must be hashable).
By default these are empty, but can be added or changed using
add_edge, add_node or direct manipulation of the attribute
dictionaries named graph, node and edge respectively.
>>> G = nx.MultiGraph(day="Friday")
>>> G.graph
{'day': 'Friday'}
Add node attributes using add_node(), add_nodes_from() or G.node
>>> G.add_node(1, time='5pm')
>>> G.add_nodes_from([3], time='2pm')
>>> G.node[1]
{'time': '5pm'}
>>> G.node[1]['room'] = 714
>>> del G.node[1]['room'] # remove attribute
>>> list(G.nodes(data=True))
[(1, {'time': '5pm'}), (3, {'time': '2pm'})]
Warning: adding a node to G.node does not add it to the graph.
Add edge attributes using add_edge(), add_edges_from(), subscript
notation, or G.edge.
>>> key = G.add_edge(1, 2, weight=4.7 )
>>> keys = G.add_edges_from([(3,4),(4,5)], color='red')
>>> keys = G.add_edges_from([(1,2,{'color':'blue'}), (2,3,{'weight':8})])
>>> G[1][2][0]['weight'] = 4.7
>>> G.edge[1][2][0]['weight'] = 4
**Shortcuts:**
Many common graph features allow python syntax to speed reporting.
>>> 1 in G # check if node in graph
True
>>> [n for n in G if n<3] # iterate through nodes
[1, 2]
>>> len(G) # number of nodes in graph
5
>>> G[1] # adjacency dict keyed by neighbor to edge attributes
... # Note: you should not change this dict manually!
{2: {0: {'weight': 4}, 1: {'color': 'blue'}}}
The fastest way to traverse all edges of a graph is via
adjacency(), but the edges() method is often more convenient.
>>> for n,nbrsdict in G.adjacency():
... for nbr,keydict in nbrsdict.items():
... for key,eattr in keydict.items():
... if 'weight' in eattr:
... (n,nbr,key,eattr['weight'])
(1, 2, 0, 4)
(2, 1, 0, 4)
(2, 3, 0, 8)
(3, 2, 0, 8)
>>> list(G.edges(data='weight', keys=True))
[(1, 2, 0, 4), (1, 2, 1, None), (2, 3, 0, 8), (3, 4, 0, None), (4, 5, 0, None)]
**Reporting:**
Simple graph information is obtained using methods.
Reporting methods usually return iterators instead of containers
to reduce memory usage.
Methods exist for reporting nodes(), edges(), neighbors() and degree()
as well as the number of nodes and edges.
For details on these and other miscellaneous methods, see below.
**Subclasses (Advanced):**
The MultiGraph class uses a dict-of-dict-of-dict-of-dict data structure.
The outer dict (node_dict) holds adjacency information keyed by node.
The next dict (adjlist_dict) represents the adjacency information and holds
edge_key dicts keyed by neighbor. The edge_key dict holds each edge_attr
dict keyed by edge key. The inner dict (edge_attr_dict) represents
the edge data and holds edge attribute values keyed by attribute names.
Each of these four dicts in the dict-of-dict-of-dict-of-dict
structure can be replaced by a user defined dict-like object.
In general, the dict-like features should be maintained but
extra features can be added. To replace one of the dicts create
a new graph class by changing the class(!) variable holding the
factory for that dict-like structure. The variable names
are node_dict_factory, adjlist_inner_dict_factory, adjlist_outer_dict_factory,
and edge_attr_dict_factory.
node_dict_factory : function, (default: dict)
Factory function to be used to create the dict containing node
attributes, keyed by node id.
It should require no arguments and return a dict-like object
adjlist_outer_dict_factory : function, (default: dict)
Factory function to be used to create the outer-most dict
in the data structure that holds adjacency info keyed by node.
It should require no arguments and return a dict-like object.
adjlist_inner_dict_factory : function, (default: dict)
Factory function to be used to create the adjacency list
dict which holds multiedge key dicts keyed by neighbor.
It should require no arguments and return a dict-like object.
edge_key_dict_factory : function, (default: dict)
Factory function to be used to create the edge key dict
which holds edge data keyed by edge key.
It should require no arguments and return a dict-like object.
edge_attr_dict_factory : function, (default: dict)
Factory function to be used to create the edge attribute
dict which holds attrbute values keyed by attribute name.
It should require no arguments and return a dict-like object.
Examples
--------
Create a multigraph subclass that tracks the order nodes are added.
>>> from collections import OrderedDict
>>> class OrderedGraph(nx.MultiGraph):
... node_dict_factory = OrderedDict
... adjlist_outer_dict_factory = OrderedDict
>>> G = OrderedGraph()
>>> G.add_nodes_from( (2,1) )
>>> list(G.nodes())
[2, 1]
>>> keys = G.add_edges_from( ((2,2), (2,1), (2,1), (1,1)) )
>>> list(G.edges())
[(2, 1), (2, 1), (2, 2), (1, 1)]
Create a multgraph object that tracks the order nodes are added
and for each node track the order that neighbors are added and for
each neighbor tracks the order that multiedges are added.
>>> class OrderedGraph(nx.MultiGraph):
... node_dict_factory = OrderedDict
... adjlist_outer_dict_factory = OrderedDict
... adjlist_inner_dict_factory = OrderedDict
... edge_key_dict_factory = OrderedDict
>>> G = OrderedGraph()
>>> G.add_nodes_from( (2,1) )
>>> list(G.nodes())
[2, 1]
>>> elist = ((2,2), (2,1,2,{'weight':0.1}), (2,1,1,{'weight':0.2}), (1,1))
>>> keys = G.add_edges_from(elist)
>>> list(G.edges(keys=True))
[(2, 2, 0), (2, 1, 2), (2, 1, 1), (1, 1, 0)]
"""
# node_dict_factory=dict # already assigned in Graph
# adjlist_outer_dict_factory=dict
# adjlist_inner_dict_factory=dict
edge_key_dict_factory = dict
# edge_attr_dict_factory=dict
[docs] def __init__(self, data=None, **attr):
self.edge_key_dict_factory = self.edge_key_dict_factory
Graph.__init__(self, data, **attr)
[docs] def new_edge_key(self, u, v):
"""Return an unused key for edges between nodes `u` and `v`.
The nodes `u` and `v` do not need to be already in the graph.
Notes
-----
In the standard MultiGraph class the new key is the number of existing
edges between `u` and `v` (increased if necessary to ensure unused).
The first edge will have key 0, then 1, etc. If an edge is removed
further new_edge_keys may not be in this order.
Parameters
----------
u, v : nodes
Returns
-------
key : int
"""
try:
keydict = self.adj[u][v]
except KeyError:
return 0
key = len(keydict)
while key in keydict:
key += 1
return key
[docs] def add_edge(self, u, v, key=None, **attr):
"""Add an edge between u and v.
The nodes u and v will be automatically added if they are
not already in the graph.
Edge attributes can be specified with keywords or by directly
accessing the edge's attribute dictionary. See examples below.
Parameters
----------
u, v : nodes
Nodes can be, for example, strings or numbers.
Nodes must be hashable (and not None) Python objects.
key : hashable identifier, optional (default=lowest unused integer)
Used to distinguish multiedges between a pair of nodes.
attr : keyword arguments, optional
Edge data (or labels or objects) can be assigned using
keyword arguments.
Returns
-------
The edge key assigned to the edge.
See Also
--------
add_edges_from : add a collection of edges
Notes
-----
To replace/update edge data, use the optional key argument
to identify a unique edge. Otherwise a new edge will be created.
NetworkX algorithms designed for weighted graphs cannot use
multigraphs directly because it is not clear how to handle
multiedge weights. Convert to Graph using edge attribute
'weight' to enable weighted graph algorithms.
Default keys are generated using the method `new_edge_key()`.
This method can be overridden by subclassing the base class and
providing a custom `new_edge_key()` method.
Examples
--------
The following all add the edge e=(1,2) to graph G:
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = (1,2)
>>> G.add_edge(1, 2) # explicit two-node form
>>> G.add_edge(*e) # single edge as tuple of two nodes
>>> G.add_edges_from( [(1,2)] ) # add edges from iterable container
Associate data to edges using keywords:
>>> G.add_edge(1, 2, weight=3)
>>> G.add_edge(1, 2, key=0, weight=4) # update data for key=0
>>> G.add_edge(1, 3, weight=7, capacity=15, length=342.7)
"""
# add nodes
if u not in self.adj:
self.adj[u] = self.adjlist_inner_dict_factory()
self.node[u] = {}
if v not in self.adj:
self.adj[v] = self.adjlist_inner_dict_factory()
self.node[v] = {}
if key is None:
key = self.new_edge_key(u, v)
if v in self.adj[u]:
keydict = self.adj[u][v]
datadict = keydict.get(key, self.edge_attr_dict_factory())
datadict.update(attr)
keydict[key] = datadict
else:
# selfloops work this way without special treatment
datadict = self.edge_attr_dict_factory()
datadict.update(attr)
keydict = self.edge_key_dict_factory()
keydict[key] = datadict
self.adj[u][v] = keydict
self.adj[v][u] = keydict
return key
[docs] def add_edges_from(self, ebunch, **attr):
"""Add all the edges in ebunch.
Parameters
----------
ebunch : container of edges
Each edge given in the container will be added to the
graph. The edges can be:
- 2-tuples (u,v) or
- 3-tuples (u,v,d) for an edge attribute dict d, or
- 4-tuples (u,v,k,d) for an edge identified by key k
attr : keyword arguments, optional
Edge data (or labels or objects) can be assigned using
keyword arguments.
Returns
-------
A list of edge keys assigned to the edges in `ebunch`.
See Also
--------
add_edge : add a single edge
add_weighted_edges_from : convenient way to add weighted edges
Notes
-----
Adding the same edge twice has no effect but any edge data
will be updated when each duplicate edge is added.
Edge attributes specified in an ebunch take precedence over
attributes specified via keyword arguments.
Default keys are generated using the method ``new_edge_key()``.
This method can be overridden by subclassing the base class and
providing a custom ``new_edge_key()`` method.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edges_from([(0,1),(1,2)]) # using a list of edge tuples
>>> e = zip(range(0,3),range(1,4))
>>> G.add_edges_from(e) # Add the path graph 0-1-2-3
Associate data to edges
>>> G.add_edges_from([(1,2),(2,3)], weight=3)
>>> G.add_edges_from([(3,4),(1,4)], label='WN2898')
"""
keylist=[]
# process ebunch
for e in ebunch:
ne = len(e)
if ne == 4:
u, v, key, dd = e
elif ne == 3:
u, v, dd = e
key = None
elif ne == 2:
u, v = e
dd = {}
key = None
else:
raise NetworkXError(
"Edge tuple %s must be a 2-tuple, 3-tuple or 4-tuple." % (e,))
ddd = {}
ddd.update(attr)
ddd.update(dd)
key = self.add_edge(u, v, key)
self[u][v][key].update(ddd)
keylist.append(key)
return keylist
[docs] def remove_edge(self, u, v, key=None):
"""Remove an edge between u and v.
Parameters
----------
u, v : nodes
Remove an edge between nodes u and v.
key : hashable identifier, optional (default=None)
Used to distinguish multiple edges between a pair of nodes.
If None remove a single (arbitrary) edge between u and v.
Raises
------
NetworkXError
If there is not an edge between u and v, or
if there is no edge with the specified key.
See Also
--------
remove_edges_from : remove a collection of edges
Examples
--------
>>> G = nx.MultiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.remove_edge(0,1)
>>> e = (1,2)
>>> G.remove_edge(*e) # unpacks e from an edge tuple
For multiple edges
>>> G = nx.MultiGraph() # or MultiDiGraph, etc
>>> G.add_edges_from([(1,2),(1,2),(1,2)]) # key_list returned
[0, 1, 2]
>>> G.remove_edge(1,2) # remove a single (arbitrary) edge
For edges with keys
>>> G = nx.MultiGraph() # or MultiDiGraph, etc
>>> G.add_edge(1,2,key='first')
'first'
>>> G.add_edge(1,2,key='second')
'second'
>>> G.remove_edge(1,2,key='second')
"""
try:
d = self.adj[u][v]
except (KeyError):
raise NetworkXError(
"The edge %s-%s is not in the graph." % (u, v))
# remove the edge with specified data
if key is None:
d.popitem()
else:
try:
del d[key]
except (KeyError):
raise NetworkXError(
"The edge %s-%s with key %s is not in the graph." % (
u, v, key))
if len(d) == 0:
# remove the key entries if last edge
del self.adj[u][v]
if u!=v: # check for selfloop
del self.adj[v][u]
[docs] def remove_edges_from(self, ebunch):
"""Remove all edges specified in ebunch.
Parameters
----------
ebunch: list or container of edge tuples
Each edge given in the list or container will be removed
from the graph. The edges can be:
- 2-tuples (u,v) All edges between u and v are removed.
- 3-tuples (u,v,key) The edge identified by key is removed.
- 4-tuples (u,v,key,data) where data is ignored.
See Also
--------
remove_edge : remove a single edge
Notes
-----
Will fail silently if an edge in ebunch is not in the graph.
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> ebunch=[(1,2),(2,3)]
>>> G.remove_edges_from(ebunch)
Removing multiple copies of edges
>>> G = nx.MultiGraph()
>>> keys = G.add_edges_from([(1,2),(1,2),(1,2)])
>>> G.remove_edges_from([(1,2),(1,2)])
>>> list(G.edges())
[(1, 2)]
>>> G.remove_edges_from([(1,2),(1,2)]) # silently ignore extra copy
>>> list(G.edges()) # now empty graph
[]
"""
for e in ebunch:
try:
self.remove_edge(*e[:3])
except NetworkXError:
pass
[docs] def has_edge(self, u, v, key=None):
"""Return True if the graph has an edge between nodes u and v.
Parameters
----------
u, v : nodes
Nodes can be, for example, strings or numbers.
key : hashable identifier, optional (default=None)
If specified return True only if the edge with
key is found.
Returns
-------
edge_ind : bool
True if edge is in the graph, False otherwise.
Examples
--------
Can be called either using two nodes u,v, an edge tuple (u,v),
or an edge tuple (u,v,key).
>>> G = nx.MultiGraph() # or MultiDiGraph
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.has_edge(0,1) # using two nodes
True
>>> e = (0,1)
>>> G.has_edge(*e) # e is a 2-tuple (u,v)
True
>>> G.add_edge(0,1,key='a')
'a'
>>> G.has_edge(0,1,key='a') # specify key
True
>>> e=(0,1,'a')
>>> G.has_edge(*e) # e is a 3-tuple (u,v,'a')
True
The following syntax are equivalent:
>>> G.has_edge(0,1)
True
>>> 1 in G[0] # though this gives :exc:`KeyError` if 0 not in G
True
"""
try:
if key is None:
return v in self.adj[u]
else:
return key in self.adj[u][v]
except KeyError:
return False
[docs] def edges(self, nbunch=None, data=False, keys=False, default=None):
"""Return an iterator over the edges.
Edges are returned as tuples with optional data and keys
in the order (node, neighbor, key, data).
Parameters
----------
nbunch : iterable container, optional (default= all nodes)
A container of nodes. The container will be iterated
through once.
data : string or bool, optional (default=False)
The edge attribute returned in 3-tuple (u,v,ddict[data]).
If True, return edge attribute dict in 3-tuple (u,v,ddict).
If False, return 2-tuple (u,v).
default : value, optional (default=None)
Value used for edges that dont have the requested attribute.
Only relevant if data is not True or False.
keys : bool, optional (default=False)
If True, return edge keys with each edge.
Returns
-------
edge : iterator
An iterator over (u,v), (u,v,d) or (u,v,key,d) tuples of edges.
Notes
-----
Nodes in nbunch that are not in the graph will be (quietly) ignored.
For directed graphs this returns the out-edges.
Examples
--------
>>> G = nx.MultiGraph() # or MultiDiGraph
>>> nx.add_path(G, [0, 1, 2])
>>> key = G.add_edge(2,3,weight=5)
>>> [e for e in G.edges()]
[(0, 1), (1, 2), (2, 3)]
>>> list(G.edges(data=True)) # default data is {} (empty dict)
[(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})]
>>> list(G.edges(data='weight', default=1))
[(0, 1, 1), (1, 2, 1), (2, 3, 5)]
>>> list(G.edges(keys=True)) # default keys are integers
[(0, 1, 0), (1, 2, 0), (2, 3, 0)]
>>> list(G.edges(data=True,keys=True)) # default keys are integers
[(0, 1, 0, {}), (1, 2, 0, {}), (2, 3, 0, {'weight': 5})]
>>> list(G.edges(data='weight',default=1,keys=True))
[(0, 1, 0, 1), (1, 2, 0, 1), (2, 3, 0, 5)]
>>> list(G.edges([0,3]))
[(0, 1), (3, 2)]
>>> list(G.edges(0))
[(0, 1)]
"""
seen = {} # helper dict to keep track of multiply stored edges
if nbunch is None:
nodes_nbrs = self.adj.items()
else:
nodes_nbrs = ((n, self.adj[n]) for n in self.nbunch_iter(nbunch))
if data is True:
for n, nbrs in nodes_nbrs:
for nbr, keydict in nbrs.items():
if nbr not in seen:
for key, ddict in keydict.items():
yield (n, nbr, key, ddict) if keys else (n, nbr, ddict)
seen[n] = 1
elif data is not False:
for n, nbrs in nodes_nbrs:
for nbr, keydict in nbrs.items():
if nbr not in seen:
for key, ddict in keydict.items():
d = ddict[data] if data in ddict else default
yield (n, nbr, key, d) if keys else (n, nbr, d)
seen[n] = 1
else:
for n, nbrs in nodes_nbrs:
for nbr, keydict in nbrs.items():
if nbr not in seen:
for key in keydict:
yield (n, nbr, key) if keys else (n, nbr)
seen[n] = 1
del seen
[docs] def get_edge_data(self, u, v, key=None, default=None):
"""Return the attribute dictionary associated with edge (u,v).
Parameters
----------
u, v : nodes
default : any Python object (default=None)
Value to return if the edge (u,v) is not found.
key : hashable identifier, optional (default=None)
Return data only for the edge with specified key.
Returns
-------
edge_dict : dictionary
The edge attribute dictionary.
Notes
-----
It is faster to use G[u][v][key].
>>> G = nx.MultiGraph() # or MultiDiGraph
>>> key = G.add_edge(0,1,key='a',weight=7)
>>> G[0][1]['a'] # key='a'
{'weight': 7}
Warning: Assigning G[u][v][key] corrupts the graph data structure.
But it is safe to assign attributes to that dictionary,
>>> G[0][1]['a']['weight'] = 10
>>> G[0][1]['a']['weight']
10
>>> G[1][0]['a']['weight']
10
Examples
--------
>>> G = nx.MultiGraph() # or MultiDiGraph
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.get_edge_data(0,1)
{0: {}}
>>> e = (0,1)
>>> G.get_edge_data(*e) # tuple form
{0: {}}
>>> G.get_edge_data('a','b',default=0) # edge not in graph, return 0
0
"""
try:
if key is None:
return self.adj[u][v]
else:
return self.adj[u][v][key]
except KeyError:
return default
[docs] def degree(self, nbunch=None, weight=None):
"""Return an iterator for (node, degree) or degree for single node.
The node degree is the number of edges adjacent to the node.
This function returns the degree for a single node or an iterator
for a bunch of nodes or if nothing is passed as argument.
Parameters
----------
nbunch : iterable container, optional (default=all nodes)
A container of nodes. The container will be iterated
through once.
weight : string or None, optional (default=None)
The edge attribute that holds the numerical value used
as a weight. If None, then each edge has weight 1.
The degree is the sum of the edge weights adjacent to the node.
Returns
-------
If a single node is requested
deg : int
Degree of the node, if a single node is passed as argument.
OR if multiple nodes are requested
nd_iter : iterator
The iterator returns two-tuples of (node, degree).
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.degree(0) # node 0 with degree 1
1
>>> list(G.degree([0,1]))
[(0, 1), (1, 2)]
"""
# Test to see if nbunch is a single node, an iterator of nodes or
# None(indicating all nodes). (nbunch in self) is True when nbunch
# is a single node.
if nbunch in self:
nbrs = self.adj[nbunch]
if weight is None:
return sum([len(data) for data in nbrs.values()]) + (nbunch in nbrs and len(nbrs[nbunch]))
deg = sum([d.get(weight, 1) for data in nbrs.values() for d in data.values()])
if nbunch in nbrs:
deg += sum([d.get(weight, 1) for key, d in nbrs[nbunch].items()])
return deg
if nbunch is None:
nodes_nbrs = self.adj.items()
else:
nodes_nbrs = ((n, self.adj[n]) for n in self.nbunch_iter(nbunch))
if weight is None:
def d_iter():
for n, nbrs in nodes_nbrs:
deg = sum([len(data) for data in nbrs.values()])
yield (n, deg + (n in nbrs and len(nbrs[n])))
else:
# edge weighted graph - degree is sum of nbr edge weights
def d_iter():
for n, nbrs in nodes_nbrs:
deg = sum([d.get(weight, 1)
for data in nbrs.values()
for d in data.values()])
if n in nbrs:
deg += sum([d.get(weight, 1)
for key, d in nbrs[n].items()])
yield (n, deg)
return d_iter()
def is_multigraph(self):
"""Return True if graph is a multigraph, False otherwise."""
return True
def is_directed(self):
"""Return True if graph is directed, False otherwise."""
return False
[docs] def to_directed(self):
"""Return a directed representation of the graph.
Returns
-------
G : MultiDiGraph
A directed graph with the same name, same nodes, and with
each edge (u,v,data) replaced by two directed edges
(u,v,data) and (v,u,data).
Notes
-----
This returns a "deepcopy" of the edge, node, and
graph attributes which attempts to completely copy
all of the data and references.
This is in contrast to the similar D=DiGraph(G) which returns a
shallow copy of the data.
See the Python copy module for more information on shallow
and deep copies, http://docs.python.org/library/copy.html.
Warning: If you have subclassed MultiGraph to use dict-like objects
in the data structure, those changes do not transfer to the MultiDiGraph
created by this method.
Examples
--------
>>> G = nx.Graph() # or MultiGraph, etc
>>> G.add_edge(0, 1)
>>> H = G.to_directed()
>>> list(H.edges())
[(0, 1), (1, 0)]
If already directed, return a (deep) copy
>>> G = nx.DiGraph() # or MultiDiGraph, etc
>>> G.add_edge(0, 1)
>>> H = G.to_directed()
>>> list(H.edges())
[(0, 1)]
"""
from networkx.classes.multidigraph import MultiDiGraph
G = MultiDiGraph()
G.add_nodes_from(self)
G.add_edges_from((u, v, key, deepcopy(datadict))
for u, nbrs in self.adjacency()
for v, keydict in nbrs.items()
for key, datadict in keydict.items())
G.graph = deepcopy(self.graph)
G.node = deepcopy(self.node)
return G
[docs] def selfloop_edges(self, data=False, keys=False, default=None):
"""Return a list of selfloop edges.
A selfloop edge has the same node at both ends.
Parameters
----------
data : bool, optional (default=False)
Return selfloop edges as two tuples (u,v) (data=False)
or three-tuples (u,v,datadict) (data=True)
or three-tuples (u,v,datavalue) (data='attrname')
default : value, optional (default=None)
Value used for edges that dont have the requested attribute.
Only relevant if data is not True or False.
keys : bool, optional (default=False)
If True, return edge keys with each edge.
Returns
-------
edgelist : list of edge tuples
A list of all selfloop edges.
See Also
--------
nodes_with_selfloops, number_of_selfloops
Examples
--------
>>> G = nx.MultiGraph() # or MultiDiGraph
>>> G.add_edge(1,1)
0
>>> G.add_edge(1,2)
0
>>> list(G.selfloop_edges())
[(1, 1)]
>>> list(G.selfloop_edges(data=True))
[(1, 1, {})]
>>> list(G.selfloop_edges(keys=True))
[(1, 1, 0)]
>>> list(G.selfloop_edges(keys=True, data=True))
[(1, 1, 0, {})]
"""
if data is True:
if keys:
return ((n, n, k, d)
for n, nbrs in self.adj.items()
if n in nbrs for k, d in nbrs[n].items())
else:
return ((n, n, d)
for n, nbrs in self.adj.items()
if n in nbrs for d in nbrs[n].values())
elif data is not False:
if keys:
return ((n, n, k, d.get(data, default))
for n, nbrs in self.adj.items()
if n in nbrs for k, d in nbrs[n].items())
else:
return ((n, n, d.get(data, default))
for n, nbrs in self.adj.items()
if n in nbrs for d in nbrs[n].values())
else:
if keys:
return ((n, n, k)
for n, nbrs in self.adj.items()
if n in nbrs for k in nbrs[n].keys())
else:
return ((n, n)
for n, nbrs in self.adj.items()
if n in nbrs for d in nbrs[n].values())
[docs] def number_of_edges(self, u=None, v=None):
"""Return the number of edges between two nodes.
Parameters
----------
u, v : nodes, optional (default=all edges)
If u and v are specified, return the number of edges between
u and v. Otherwise return the total number of all edges.
Returns
-------
nedges : int
The number of edges in the graph. If nodes u and v are specified
return the number of edges between those nodes.
See Also
--------
size
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.number_of_edges()
3
>>> G.number_of_edges(0,1)
1
>>> e = (0,1)
>>> G.number_of_edges(*e)
1
"""
if u is None: return self.size()
try:
edgedata = self.adj[u][v]
except KeyError:
return 0 # no such edge
return len(edgedata)
[docs] def subgraph(self, nbunch):
"""Return the subgraph induced on nodes in nbunch.
The induced subgraph of the graph contains the nodes in nbunch
and the edges between those nodes.
Parameters
----------
nbunch : list, iterable
A container of nodes which will be iterated through once.
Returns
-------
G : Graph
A subgraph of the graph with the same edge attributes.
Notes
-----
The graph, edge or node attributes just point to the original graph.
So changes to the node or edge structure will not be reflected in
the original graph while changes to the attributes will.
To create a subgraph with its own copy of the edge/node attributes use:
nx.Graph(G.subgraph(nbunch))
If edge attributes are containers, a deep copy can be obtained using:
G.subgraph(nbunch).copy()
For an inplace reduction of a graph to a subgraph you can remove nodes:
G.remove_nodes_from([ n in G if n not in set(nbunch)])
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2, 3])
>>> H = G.subgraph([0,1,2])
>>> list(H.edges())
[(0, 1), (1, 2)]
"""
bunch = self.nbunch_iter(nbunch)
# create new graph and copy subgraph into it
H = self.__class__()
# copy node and attribute dictionaries
for n in bunch:
H.node[n] = self.node[n]
# namespace shortcuts for speed
H_adj = H.adj
self_adj = self.adj
# add nodes and edges (undirected method)
for n in H:
Hnbrs = H.adjlist_inner_dict_factory()
H_adj[n] = Hnbrs
for nbr, edgedict in self_adj[n].items():
if nbr in H_adj:
# add both representations of edge: n-nbr and nbr-n
# they share the same edgedict
ed = edgedict.copy()
Hnbrs[nbr] = ed
H_adj[nbr][n] = ed
H.graph = self.graph
return H
[docs] def edge_subgraph(self, edges):
"""Returns the subgraph induced by the specified edges.
The induced subgraph contains each edge in `edges` and each
node incident to any one of those edges.
Parameters
----------
edges : iterable
An iterable of edges in this graph.
Returns
-------
G : Graph
An edge-induced subgraph of this graph with the same edge
attributes.
Notes
-----
The graph, edge, and node attributes in the returned subgraph
are references to the corresponding attributes in the original
graph. Thus changes to the node or edge structure of the
returned graph will not be reflected in the original graph, but
changes to the attributes will.
To create a subgraph with its own copy of the edge or node
attributes, use::
>>> nx.MultiGraph(G.edge_subgraph(edges)) # doctest: +SKIP
If edge attributes are containers, a deep copy of the attributes
can be obtained using::
>>> G.edge_subgraph(edges).copy() # doctest: +SKIP
Examples
--------
Get a subgraph induced by only those edges that have a certain
attribute::
>>> # Create a graph in which some edges are "good" and some "bad".
>>> G = nx.MultiGraph()
>>> key = G.add_edge(0, 1, key=0, good=True)
>>> key = G.add_edge(0, 1, key=1, good=False)
>>> key = G.add_edge(1, 2, key=0, good=False)
>>> key = G.add_edge(1, 2, key=1, good=True)
>>> # Keep only those edges that are marked as "good".
>>> edges = G.edges(keys=True, data='good')
>>> edges = ((u, v, k) for (u, v, k, good) in edges if good)
>>> H = G.edge_subgraph(edges)
>>> list(H.edges(keys=True, data=True))
[(0, 1, 0, {'good': True}), (1, 2, 1, {'good': True})]
"""
H = self.__class__()
adj = self.adj
# Filter out edges that don't correspond to nodes in the graph.
def is_in_graph(u, v, k):
return u in adj and v in adj[u] and k in adj[u][v]
edges = (e for e in edges if is_in_graph(*e))
for u, v, k in edges:
# Copy the node attributes if they haven't been copied
# already.
if u not in H.node:
H.node[u] = self.node[u]
if v not in H.node:
H.node[v] = self.node[v]
# Create an entry in the adjacency dictionary for the
# nodes u and v if they don't exist yet.
if u not in H.adj:
H.adj[u] = H.adjlist_inner_dict_factory()
if v not in H.adj:
H.adj[v] = H.adjlist_inner_dict_factory()
# Create an entry in the edge dictionary for the edges (u,
# v) and (v, u) if the don't exist yet.
if v not in H.adj[u]:
H.adj[u][v] = H.edge_key_dict_factory()
if u not in H.adj[v]:
H.adj[v][u] = H.edge_key_dict_factory()
# Copy the edge attributes.
H.edge[u][v][k] = self.edge[u][v][k]
H.edge[v][u][k] = self.edge[v][u][k]
H.graph = self.graph
return H