Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.classes.multigraph

"""Base class for MultiGraph."""
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
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 an edge list, or any
NetworkX graph object.  If the corresponding optional Python
packages are installed the data can also be a NumPy matrix
or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz graph.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to graph as key=value pairs.

--------
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:

Add the nodes from any container (a list, dict, set or
even the lines from a file or the nodes from another graph).

>>> H=nx.Graph()

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.

**Edges:**

G can also be grown by adding edges.

a list of edges,

or a collection of edges,

If some edges connect nodes not yet in the graph, the nodes
edge is created and stored using a key to identify the edge.
By default the key is the lowest unused integer.

>>> G
{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
dictionaries named graph, node and edge respectively.

>>> G = nx.MultiGraph(day="Friday")
>>> G.graph
{'day': 'Friday'}

>>> G.node
{'time': '5pm'}
>>> G.node['room'] = 714
>>> del G.node['room'] # remove attribute
>>> G.nodes(data=True)
[(1, {'time': '5pm'}), (3, {'time': '2pm'})]

Warning: adding a node to G.node does not add it to the graph.

notation, or G.edge.

>>> G['weight'] = 4.7
>>> G.edge['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 # 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_iter(), but the edges() method is often more convenient.

...     for nbr,keydict in nbrsdict.items():
...        for key,eattr in keydict.items():
...            if 'weight' in eattr:
...                (n,nbr,eattr['weight'])
(1, 2, 4)
(2, 1, 4)
(2, 3, 8)
(3, 2, 8)
>>> [ (u,v,edata['weight']) for u,v,edata in G.edges(data=True) if 'weight' in edata ]
[(1, 2, 4), (2, 3, 8)]

**Reporting:**

Simple graph information is obtained using methods.
Iterator versions of many reporting methods exist for efficiency.
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.
"""
[docs]    def add_edge(self, u, v, key=None, attr_dict=None, **attr):
"""Add an edge between u and v.

The nodes u and v will be automatically added if they are

Edge attributes can be specified with keywords or by providing
a dictionary with key/value pairs.  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_dict : dictionary, optional (default= no attributes)
Dictionary of edge attributes.  Key/value pairs will
update existing data associated with the edge.
attr : keyword arguments, optional
Edge data (or labels or objects) can be assigned using
keyword arguments.

--------

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.

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

Associate data to edges using keywords:

>>> 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)
"""
# set up attribute dict
if attr_dict is None:
attr_dict=attr
else:
try:
attr_dict.update(attr)
except AttributeError:
raise NetworkXError(\
"The attr_dict argument must be a dictionary.")
self.node[u] = {}
self.node[v] = {}
if key is None:
# find a unique integer key
# other methods might be better here?
key=len(keydict)
while key in keydict:
key+=1
else:
# selfloops work this way without special treatment
if key is None:
key=0

[docs]    def add_edges_from(self, ebunch, attr_dict=None, **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_dict : dictionary, optional  (default= no attributes)
Dictionary of edge attributes.  Key/value pairs will
update existing data associated with each edge.
attr : keyword arguments, optional
Edge data (or labels or objects) can be assigned using
keyword arguments.

--------

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 edges as a tuple take precedence
over attributes specified generally.

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))

Associate data to edges

"""
# set up attribute dict
if attr_dict is None:
attr_dict=attr
else:
try:
attr_dict.update(attr)
except AttributeError:
raise NetworkXError(\
"The attr_dict argument must be a dictionary.")
# 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,))
else:
keydict={}
if key is None:
# find a unique integer key
# other methods might be better here?
key=len(keydict)
while key in keydict:
key+=1

[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 (abritrary) 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.

--------
remove_edges_from : remove a collection of edges

Examples
--------
>>> G = nx.MultiGraph()
>>> 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.remove_edge(1,2) # remove a single (arbitrary) edge

For edges with keys

>>> G = nx.MultiGraph()   # or MultiDiGraph, etc
>>> G.remove_edge(1,2,key='second')

"""
try:
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
if u!=v:  # check for selfloop

[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.

--------
remove_edge : remove a single edge

Notes
-----
Will fail silently if an edge in ebunch is not in the graph.

Examples
--------
>>> G = nx.MultiGraph() # or MultiDiGraph
>>> ebunch=[(1,2),(2,3)]
>>> G.remove_edges_from(ebunch)

Removing multiple copies of edges

>>> G = nx.MultiGraph()
>>> G.remove_edges_from([(1,2),(1,2)])
>>> G.edges()
[(1, 2)]
>>> G.remove_edges_from([(1,2),(1,2)]) # silently ignore extra copy
>>> 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
>>> 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.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  # though this gives KeyError if 0 not in G
True

"""
try:
if key is None:
else:
except KeyError:
return False

[docs]    def edges(self, nbunch=None, data=False, keys=False):
"""Return a list of 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 : bool, optional (default=False)
Return two tuples (u,v) (False) or three-tuples (u,v,data) (True).
keys : bool, optional (default=False)
Return two tuples (u,v) (False) or three-tuples (u,v,key) (True).

Returns
--------
edge_list: list of edge tuples
Edges that are adjacent to any node in nbunch, or a list
of all edges if nbunch is not specified.

--------
edges_iter : return an iterator over the 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
>>> G.edges()
[(0, 1), (1, 2), (2, 3)]
>>> G.edges(data=True) # default edge data is {} (empty dictionary)
[(0, 1, {}), (1, 2, {}), (2, 3, {})]
>>> G.edges(keys=True) # default keys are integers
[(0, 1, 0), (1, 2, 0), (2, 3, 0)]
>>> G.edges(data=True,keys=True) # default keys are integers
[(0, 1, 0, {}), (1, 2, 0, {}), (2, 3, 0, {})]
>>> G.edges([0,3])
[(0, 1), (3, 2)]
>>> G.edges(0)
[(0, 1)]

"""
return list(self.edges_iter(nbunch, data=data,keys=keys))

[docs]    def edges_iter(self, nbunch=None, data=False, keys=False):
"""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 : bool, optional (default=False)
If True, return edge attribute dict with each edge.
keys : bool, optional (default=False)
If True, return edge keys with each edge.

Returns
-------
edge_iter : iterator
An iterator of (u,v), (u,v,d) or (u,v,key,d) tuples of edges.

--------
edges : return a list 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
>>> [e for e in G.edges_iter()]
[(0, 1), (1, 2), (2, 3)]
>>> list(G.edges_iter(data=True)) # default data is {} (empty dict)
[(0, 1, {}), (1, 2, {}), (2, 3, {})]
>>> 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, {})]
>>> list(G.edges_iter([0,3]))
[(0, 1), (3, 2)]
>>> list(G.edges_iter(0))
[(0, 1)]

"""
seen={}     # helper dict to keep track of multiply stored edges
if nbunch is None:
else:
if data:
for n,nbrs in nodes_nbrs:
for nbr,keydict in nbrs.items():
if nbr not in seen:
for key,data in keydict.items():
if keys:
yield (n,nbr,key,data)
else:
yield (n,nbr,data)
seen[n]=1
else:
for n,nbrs in nodes_nbrs:
for nbr,keydict in nbrs.items():
if nbr not in seen:
for key,data in keydict.items():
if keys:
yield (n,nbr,key)
else:
yield (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)
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
>>> G['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['a']['weight'] = 10
>>> G['a']['weight']
10
>>> G['a']['weight']
10

Examples
--------
>>> G = nx.MultiGraph() # or MultiDiGraph
>>> 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:
else:
except KeyError:
return default

[docs]    def degree_iter(self, nbunch=None, weight=None):
"""Return an iterator for (node, degree).

The node degree is the number of edges adjacent to the node.

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
-------
nd_iter : an iterator
The iterator returns two-tuples of (node, degree).

--------
degree

Examples
--------
>>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> list(G.degree_iter(0)) # node 0 with degree 1
[(0, 1)]
>>> list(G.degree_iter([0,1]))
[(0, 1), (1, 2)]

"""
if nbunch is None:
else:

if weight is None:
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
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)

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.

and deep copies, http://docs.python.org/library/copy.html.

Examples
--------
>>> G = nx.Graph()   # or MultiGraph, etc
>>> H = G.to_directed()
>>> H.edges()
[(0, 1), (1, 0)]

If already directed, return a (deep) copy

>>> G = nx.DiGraph()   # or MultiDiGraph, etc
>>> H = G.to_directed()
>>> H.edges()
[(0, 1)]
"""
from networkx.classes.multidigraph import MultiDiGraph
G=MultiDiGraph()
for v,keydict in nbrs.items()
G.graph=deepcopy(self.graph)
G.node=deepcopy(self.node)
return G

[docs]    def selfloop_edges(self, data=False, keys=False):
"""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,data) (data=True)
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.

--------
nodes_with_selfloops, number_of_selfloops

Examples
--------
>>> G = nx.MultiGraph()   # or MultiDiGraph
>>> G.selfloop_edges()
[(1, 1)]
>>> G.selfloop_edges(data=True)
[(1, 1, {})]
>>> G.selfloop_edges(keys=True)
[(1, 1, 0)]
>>> G.selfloop_edges(keys=True, data=True)
[(1, 1, 0, {})]
"""
if data:
if keys:
return [ (n,n,k,d)
if n in nbrs for k,d in nbrs[n].items()]
else:
return [ (n,n,d)
if n in nbrs for d in nbrs[n].values()]
else:
if keys:
return [ (n,n,k)
if n in nbrs for k in nbrs[n].keys()]

else:
return [ (n,n)
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.

--------
size

Examples
--------
>>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> 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:
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
>>> H = G.subgraph([0,1,2])
>>> 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
# add nodes and edges (undirected method)
for n in H:
Hnbrs={}