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.multidigraph
"""Base class for MultiDiGraph."""
# Copyright (C) 2004-2011 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 # for doctests
from networkx.classes.digraph import DiGraph
from networkx.classes.multigraph import MultiGraph
from networkx.exception import NetworkXError
__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Dan Schult(dschult@colgate.edu)'])
[docs]class MultiDiGraph(MultiGraph,DiGraph):
"""A directed graph class that can store multiedges.
Multiedges are multiple edges between two nodes. Each edge
can hold optional data or attributes.
A MultiDiGraph holds directed 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.
See Also
--------
Graph
DiGraph
MultiGraph
Examples
--------
Create an empty graph structure (a "null graph") with no nodes and
no edges.
>>> G = nx.MultiDiGraph()
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.Graph()
>>> H.add_path([0,1,2,3,4,5,6,7,8,9])
>>> 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,
>>> G.add_edge(1, 2)
a list of edges,
>>> G.add_edges_from([(1,2),(1,3)])
or a collection of edges,
>>> G.add_edges_from(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.
>>> G.add_edges_from([(4,5,dict(route=282)), (4,5,dict(route=37))])
>>> G[4]
{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.MultiDiGraph(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
>>> 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.
>>> G.add_edge(1, 2, weight=4.7 )
>>> G.add_edges_from([(3,4),(4,5)], color='red')
>>> 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_iter(), but the edges() method is often more convenient.
>>> for n,nbrsdict in G.adjacency_iter():
... for nbr,keydict in nbrsdict.items():
... for key,eattr in keydict.items():
... if 'weight' in eattr:
... (n,nbr,eattr['weight'])
(1, 2, 4)
(2, 3, 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
not already in the graph.
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.
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.
Examples
--------
The following all add the edge e=(1,2) to graph G:
>>> G = nx.MultiDiGraph()
>>> 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)
"""
# 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.")
# add nodes
if u not in self.succ:
self.succ[u] = {}
self.pred[u] = {}
self.node[u] = {}
if v not in self.succ:
self.succ[v] = {}
self.pred[v] = {}
self.node[v] = {}
if v in self.succ[u]:
keydict=self.adj[u][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
datadict=keydict.get(key,{})
datadict.update(attr_dict)
keydict[key]=datadict
else:
# selfloops work this way without special treatment
if key is None:
key=0
datadict={}
datadict.update(attr_dict)
keydict={key:datadict}
self.succ[u][v] = keydict
self.pred[v][u] = keydict
[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.
See Also
--------
remove_edges_from : remove a collection of edges
Examples
--------
>>> G = nx.MultiDiGraph()
>>> G.add_path([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.MultiDiGraph()
>>> G.add_edges_from([(1,2),(1,2),(1,2)])
>>> G.remove_edge(1,2) # remove a single (arbitrary) edge
For edges with keys
>>> G = nx.MultiDiGraph()
>>> G.add_edge(1,2,key='first')
>>> G.add_edge(1,2,key='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.succ[u][v]
del self.pred[v][u]
[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.
See Also
--------
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.MultiDiGraph()
>>> G.add_path([0,1,2,3])
>>> [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_iter([0,2]))
[(0, 1), (2, 3)]
>>> list(G.edges_iter(0))
[(0, 1)]
"""
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:
for n,nbrs in nodes_nbrs:
for nbr,keydict in nbrs.items():
for key,data in keydict.items():
if keys:
yield (n,nbr,key,data)
else:
yield (n,nbr,data)
else:
for n,nbrs in nodes_nbrs:
for nbr,keydict in nbrs.items():
for key,data in keydict.items():
if keys:
yield (n,nbr,key)
else:
yield (n,nbr)
# alias out_edges to edges
out_edges_iter=edges_iter
[docs] def out_edges(self, nbunch=None, keys=False, data=False):
"""Return a list of the outgoing 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
-------
out_edges : list
An listr of (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 edges() is the same as out_edges().
See Also
--------
in_edges: return a list of incoming edges
"""
return list(self.out_edges_iter(nbunch, keys=keys, data=data))
[docs] def in_edges_iter(self, nbunch=None, data=False, keys=False):
"""Return an iterator over the incoming edges.
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
-------
in_edge_iter : iterator
An iterator of (u,v), (u,v,d) or (u,v,key,d) tuples of edges.
See Also
--------
edges_iter : return an iterator of edges
"""
if nbunch is None:
nodes_nbrs=self.pred.items()
else:
nodes_nbrs=((n,self.pred[n]) for n in self.nbunch_iter(nbunch))
if data:
for n,nbrs in nodes_nbrs:
for nbr,keydict in nbrs.items():
for key,data in keydict.items():
if keys:
yield (nbr,n,key,data)
else:
yield (nbr,n,data)
else:
for n,nbrs in nodes_nbrs:
for nbr,keydict in nbrs.items():
for key,data in keydict.items():
if keys:
yield (nbr,n,key)
else:
yield (nbr,n)
[docs] def in_edges(self, nbunch=None, keys=False, data=False):
"""Return a list of the incoming edges.
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
-------
in_edges : list
A list of (u,v), (u,v,d) or (u,v,key,d) tuples of edges.
See Also
--------
out_edges: return a list of outgoing edges
"""
return list(self.in_edges_iter(nbunch, keys=keys, data=data))
[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.
Returns
-------
nd_iter : an iterator
The iterator returns two-tuples of (node, degree).
See Also
--------
degree
Examples
--------
>>> G = nx.MultiDiGraph()
>>> G.add_path([0,1,2,3])
>>> 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:
nodes_nbrs=zip(iter(self.succ.items()),iter(self.pred.items()))
else:
nodes_nbrs=zip(
((n,self.succ[n]) for n in self.nbunch_iter(nbunch)),
((n,self.pred[n]) for n in self.nbunch_iter(nbunch)))
if weight is None:
for (n,succ),(n2,pred) in nodes_nbrs:
indeg = sum([len(data) for data in pred.values()])
outdeg = sum([len(data) for data in succ.values()])
yield (n, indeg + outdeg)
else:
# edge weighted graph - degree is sum of nbr edge weights
for (n,succ),(n2,pred) in nodes_nbrs:
deg = sum([d.get(weight,1)
for data in pred.values()
for d in data.values()])
deg += sum([d.get(weight,1)
for data in succ.values()
for d in data.values()])
yield (n, deg)
[docs] def in_degree_iter(self, nbunch=None, weight=None):
"""Return an iterator for (node, in-degree).
The node in-degree is the number of edges pointing in 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, in-degree).
See Also
--------
degree, in_degree, out_degree, out_degree_iter
Examples
--------
>>> G = nx.MultiDiGraph()
>>> G.add_path([0,1,2,3])
>>> list(G.in_degree_iter(0)) # node 0 with degree 0
[(0, 0)]
>>> list(G.in_degree_iter([0,1]))
[(0, 0), (1, 1)]
"""
if nbunch is None:
nodes_nbrs=self.pred.items()
else:
nodes_nbrs=((n,self.pred[n]) for n in self.nbunch_iter(nbunch))
if weight is None:
for n,nbrs in nodes_nbrs:
yield (n, sum([len(data) for data in nbrs.values()]) )
else:
# edge weighted graph - degree is sum of nbr edge weights
for n,pred in nodes_nbrs:
deg = sum([d.get(weight,1)
for data in pred.values()
for d in data.values()])
yield (n, deg)
[docs] def out_degree_iter(self, nbunch=None, weight=None):
"""Return an iterator for (node, out-degree).
The node out-degree is the number of edges pointing out of 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.
Returns
-------
nd_iter : an iterator
The iterator returns two-tuples of (node, out-degree).
See Also
--------
degree, in_degree, out_degree, in_degree_iter
Examples
--------
>>> G = nx.MultiDiGraph()
>>> G.add_path([0,1,2,3])
>>> list(G.out_degree_iter(0)) # node 0 with degree 1
[(0, 1)]
>>> list(G.out_degree_iter([0,1]))
[(0, 1), (1, 1)]
"""
if nbunch is None:
nodes_nbrs=self.succ.items()
else:
nodes_nbrs=((n,self.succ[n]) for n in self.nbunch_iter(nbunch))
if weight is None:
for n,nbrs in nodes_nbrs:
yield (n, sum([len(data) for data in nbrs.values()]) )
else:
for n,succ in nodes_nbrs:
deg = sum([d.get(weight,1)
for data in succ.values()
for d in data.values()])
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 True
[docs] def to_directed(self):
"""Return a directed copy of the graph.
Returns
-------
G : MultiDiGraph
A deepcopy of the graph.
Notes
-----
If edges in both directions (u,v) and (v,u) exist in the
graph, attributes for the new undirected edge will be a combination of
the attributes of the directed edges. The edge data is updated
in the (arbitrary) order that the edges are encountered. For
more customized control of the edge attributes use add_edge().
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 G=DiGraph(D) 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.
Examples
--------
>>> G = nx.Graph() # or MultiGraph, etc
>>> G.add_path([0,1])
>>> H = G.to_directed()
>>> H.edges()
[(0, 1), (1, 0)]
If already directed, return a (deep) copy
>>> G = nx.MultiDiGraph()
>>> G.add_path([0,1])
>>> H = G.to_directed()
>>> H.edges()
[(0, 1)]
"""
return deepcopy(self)
[docs] def to_undirected(self, reciprocal=False):
"""Return an undirected representation of the digraph.
Parameters
----------
reciprocal : bool (optional)
If True only keep edges that appear in both directions
in the original digraph.
Returns
-------
G : MultiGraph
An undirected graph with the same name and nodes and
with edge (u,v,data) if either (u,v,data) or (v,u,data)
is in the digraph. If both edges exist in digraph and
their edge data is different, only one edge is created
with an arbitrary choice of which edge data to use.
You must check and correct for this manually if desired.
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.
"""
H=MultiGraph()
H.name=self.name
H.add_nodes_from(self)
if reciprocal is True:
H.add_edges_from( (u,v,key,deepcopy(data))
for u,nbrs in self.adjacency_iter()
for v,keydict in nbrs.items()
for key,data in keydict.items()
if self.has_edge(v,u,key))
else:
H.add_edges_from( (u,v,key,deepcopy(data))
for u,nbrs in self.adjacency_iter()
for v,keydict in nbrs.items()
for key,data in keydict.items())
H.graph=deepcopy(self.graph)
H.node=deepcopy(self.node)
return H
[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
>>> G.add_path([0,1,2,3])
>>> 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
H_succ=H.succ
H_pred=H.pred
self_succ=self.succ
self_pred=self.pred
# add nodes
for n in H:
H_succ[n]={}
H_pred[n]={}
# add edges
for u in H_succ:
Hnbrs=H_succ[u]
for v,edgedict in self_succ[u].items():
if v in H_succ:
# add both representations of edge: u-v and v-u
# they share the same edgedict
ed=edgedict.copy()
Hnbrs[v]=ed
H_pred[v][u]=ed
H.graph=self.graph
return H
[docs] def reverse(self, copy=True):
"""Return the reverse of the graph.
The reverse is a graph with the same nodes and edges
but with the directions of the edges reversed.
Parameters
----------
copy : bool optional (default=True)
If True, return a new DiGraph holding the reversed edges.
If False, reverse the reverse graph is created using
the original graph (this changes the original graph).
"""
if copy:
H = self.__class__(name="Reverse of (%s)"%self.name)
H.add_nodes_from(self)
H.add_edges_from( (v,u,k,deepcopy(d)) for u,v,k,d
in self.edges(keys=True, data=True) )
H.graph=deepcopy(self.graph)
H.node=deepcopy(self.node)
else:
self.pred,self.succ=self.succ,self.pred
self.adj=self.succ
H=self
return H