"""
Base class for undirected graphs.
The Graph class allows any hashable object as a node
and can associate key/value attribute pairs with each undirected edge.
Self-loops are allowed but multiple edges are not (see MultiGraph).
For directed graphs see DiGraph and MultiDiGraph.
"""
__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Dan Schult(dschult@colgate.edu)'])
# Copyright (C) 2004-2009 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
#
__docformat__ = "restructuredtext en"
import networkx as nx
from networkx.exception import NetworkXException,NetworkXError
import networkx.convert as convert
from copy import deepcopy
class Graph(object):
"""
Base class for undirected graphs.
A Graph stores nodes and edges with optional data, or attributes.
Graphs hold undirected edges. Self loops are allowed but multiple
(parallel) edges are not.
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.
name : string, optional (default='')
An optional name for the graph.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to graph as key=value pairs.
See Also
--------
DiGraph
MultiGraph
MultiDiGraph
Examples
--------
Create an empty graph structure (a "null graph") with no nodes and
no edges.
>>> G = nx.Graph()
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,
>>> 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. There are no errors when adding
nodes or edges that already exist.
**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.Graph(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
>>> G.nodes(data=True)
[(1, {'room': 714, '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]['weight'] = 4.7
>>> G.edge[1][2]['weight'] = 4
**Shortcuts:**
Many common graph features allow python syntax to speed reporting.
>>> 1 in G # check if node in graph
True
>>> print [n for n in G if n<3] # iterate through nodes
[1, 2]
>>> print len(G) # number of nodes in graph
5
>>> print G[1] # adjacency dict keyed by neighbor to edge attributes
... # Note: you should not change this dict manually!
{2: {'color': 'blue', 'weight': 4}}
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,eattr in nbrsdict.iteritems():
... if 'weight' in eattr:
... print (n,nbr,eattr['weight'])
(1, 2, 4)
(2, 1, 4)
(2, 3, 8)
(3, 2, 8)
>>> print [ (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.
"""
def __init__(self, data=None, name='', **attr):
"""Initialize a graph with edges, name, graph 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.
name : string, optional (default='')
An optional name for the graph.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to graph as key=value pairs.
See Also
--------
convert
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G = nx.Graph(name='my graph')
>>> e = [(1,2),(2,3),(3,4)] # list of edges
>>> G = nx.Graph(e)
Arbitrary graph attribute pairs (key=value) may be assigned
>>> G=nx.Graph(e, day="Friday")
>>> G.graph
{'day': 'Friday'}
"""
self.graph = {} # dictionary for graph attributes
self.node = {} # empty node dict (created before convert)
self.adj = {} # empty adjacency dict
if data is not None: # attempt to load graph with data
convert.to_networkx_graph(data,create_using=self)
# load graph attributes (must be after convert)
self.graph.update(attr)
self.name = name
self.edge = self.adj
def __str__(self):
"""Return the graph name.
Returns
-------
name : string
The name of the graph.
Examples
--------
>>> G = nx.path_graph(4)
>>> print G
path_graph(4)
"""
return self.name
def __iter__(self):
"""Iterate over the nodes. Use the expression 'for n in G'.
Returns
-------
niter : iterator
An iterator over all nodes in the graph.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> for n in G:
... print n,
0 1 2 3
"""
return self.adj.iterkeys()
def __contains__(self,n):
"""Return True if n is a node, False otherwise. Use the expression
'n in G'.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> print 1 in G
True
"""
try:
return n in self.adj
except TypeError:
return False
def __len__(self):
"""Return the number of nodes. Use the expression 'len(G)'.
Returns
-------
nnodes : int
The number of nodes in the graph.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> print len(G)
4
"""
return len(self.adj)
def __getitem__(self, n):
"""Return a dict of neighbors of node n. Use the expression 'G[n]'.
Parameters
----------
n : node
A node in the graph.
Returns
-------
adj_dict : dictionary
The adjacency dictionary for nodes connected to n.
Notes
-----
G[n] is similar to G.neighbors(n) but the internal data dictionary
is returned instead of a list.
Assigning G[n] will corrupt the internal graph data structure.
Use G[n] for reading data only.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> print G[0]
{1: {}}
"""
return self.adj[n]
def add_node(self, n, attr_dict=None, **attr):
"""Add a single node n and update node attributes.
Parameters
----------
n : node
A node can be any hashable Python object except None.
attr_dict : dictionary, optional (default= no attributes)
Dictionary of node attributes. Key/value pairs will
update existing data associated with the node.
attr : keyword arguments, optional
Set or change attributes using key=value.
See Also
--------
add_nodes_from
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_node(1)
>>> G.add_node('Hello')
>>> K3 = nx.Graph([(0,1),(1,2),(2,0)])
>>> G.add_node(K3)
>>> G.number_of_nodes()
3
Use keywords set/change node attributes:
>>> G.add_node(1,size=10)
>>> G.add_node(3,weight=0.4,UTM=('13S',382871,3972649))
Notes
-----
A hashable object is one that can be used as a key in a Python
dictionary. This includes strings, numbers, tuples of strings
and numbers, etc.
On many platforms hashable items also include mutables such as
NetworkX Graphs, though one should be careful that the hash
doesn't change on mutables.
"""
# 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.")
if n not in self.adj:
self.adj[n] = {}
self.node[n] = attr_dict
else: # update attr even if node already exists
self.node[n].update(attr_dict)
def add_nodes_from(self, nodes, **attr):
"""Add multiple nodes.
Parameters
----------
nodes : iterable container
A container of nodes (list, dict, set, etc.).
OR
A container of (node, attribute dict) tuples.
Node attributes are updated using the attribute dict.
attr : keyword arguments, optional (default= no attributes)
Update attributes for all nodes in nodes.
Node attributes specified in nodes as a tuple
take precedence over attributes specified generally.
See Also
--------
add_node
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_nodes_from('Hello')
>>> K3 = nx.Graph([(0,1),(1,2),(2,0)])
>>> G.add_nodes_from(K3)
>>> sorted(G.nodes())
[0, 1, 2, 'H', 'e', 'l', 'o']
Use keywords to update specific node attributes for every node.
>>> G.add_nodes_from([1,2], size=10)
>>> G.add_nodes_from([3,4], weight=0.4)
Use (node, attrdict) tuples to update attributes for specific
nodes.
>>> G.add_nodes_from([(1,dict(size=11)), (2,{'color':'blue'})])
>>> G.node[1]['size']
11
>>> H = nx.Graph()
>>> H.add_nodes_from(G.nodes(data=True))
>>> H.node[1]['size']
11
"""
for n in nodes:
try:
newnode=n not in self.adj
except TypeError:
nn,ndict = n
if nn not in self.adj:
self.adj[nn] = {}
newdict = attr.copy()
newdict.update(ndict)
self.node[nn] = newdict
else:
olddict = self.node[nn]
olddict.update(attr)
olddict.update(ndict)
continue
if newnode:
self.adj[n] = {}
self.node[n] = attr.copy()
else:
self.node[n].update(attr)
def remove_node(self,n):
"""Remove node n.
Removes the node n and all adjacent edges.
Attempting to remove a non-existent node will raise an exception.
Parameters
----------
n : node
A node in the graph
Raises
-------
NetworkXError
If n is not in the graph.
See Also
--------
remove_nodes_from
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2])
>>> G.edges()
[(0, 1), (1, 2)]
>>> G.remove_node(1)
>>> G.edges()
[]
"""
adj = self.adj
try:
nbrs = adj[n].keys() # keys handles self-loops (allow mutation later)
del self.node[n]
except KeyError: # NetworkXError if n not in self
raise NetworkXError("The node %s is not in the graph."%(n,))
for u in nbrs:
del adj[u][n] # remove all edges n-u in graph
del adj[n] # now remove node
def remove_nodes_from(self, nodes):
"""Remove multiple nodes.
Parameters
----------
nodes : iterable container
A container of nodes (list, dict, set, etc.). If a node
in the container is not in the graph it is silently
ignored.
See Also
--------
remove_node
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2])
>>> e = G.nodes()
>>> e
[0, 1, 2]
>>> G.remove_nodes_from(e)
>>> G.nodes()
[]
"""
adj = self.adj
for n in nodes:
try:
del self.node[n]
for u in adj[n].keys(): # keys() handles self-loops
del adj[u][n] #(allows mutation of dict in loop)
del adj[n]
except KeyError:
pass
def nodes_iter(self, data=False):
"""Return an iterator over the nodes.
Parameters
----------
data : boolean, optional (default=False)
If False the iterator returns nodes. If True
return a two-tuple of node and node data dictionary
Returns
-------
niter : iterator
An iterator over nodes. If data=True the iterator gives
two-tuples containing (node, node data, dictionary)
Notes
-----
If the node data is not required it is simpler and equivalent
to use the expression 'for n in G'.
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2])
>>> for n in G:
... print n,
0 1 2
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2])
>>> for n in G.nodes_iter():
... print n,
0 1 2
>>> for n,d in G.nodes_iter(data=True):
... print d,
{} {} {}
"""
if data:
return self.node.iteritems()
return self.adj.iterkeys()
def nodes(self, data=False):
"""Return a list of the nodes in the graph.
Parameters
----------
data : boolean, optional (default=False)
If False return a list of nodes. If True return a
two-tuple of node and node data dictionary
Returns
-------
nlist : list
A list of nodes. If data=True a list of two-tuples containing
(node, node data dictionary).
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2])
>>> print G.nodes()
[0, 1, 2]
>>> G.add_node(1, time='5pm')
>>> print G.nodes(data=True)
[(0, {}), (1, {'time': '5pm'}), (2, {})]
"""
return list(self.nodes_iter(data=data))
def number_of_nodes(self):
"""Return the number of nodes in the graph.
Returns
-------
nnodes : int
The number of nodes in the graph.
See Also
--------
order, __len__ which are identical
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2])
>>> print len(G)
3
"""
return len(self.adj)
def order(self):
"""Return the number of nodes in the graph.
Returns
-------
nnodes : int
The number of nodes in the graph.
See Also
--------
number_of_nodes, __len__ which are identical
"""
return len(self.adj)
def has_node(self, n):
"""Return True if the graph contains the node n.
Parameters
----------
n : node
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2])
>>> print G.has_node(0)
True
It is more readable and simpler to use
>>> 0 in G
True
"""
try:
return n in self.adj
except TypeError:
return False
def add_edge(self, u, v, 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.
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
-----
Adding an edge that already exists updates the edge data.
NetworkX algorithms designed for weighted graphs use as
the edge weight a numerical value assigned to the keyword
'weight'.
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, 3, weight=7, capacity=15, length=342.7)
"""
# set up attribute dictionary
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.adj:
self.adj[u] = {}
self.node[u] = {}
if v not in self.adj:
self.adj[v] = {}
self.node[v] = {}
# add the edge
datadict=self.adj[u].get(v,{})
datadict.update(attr_dict)
self.adj[u][v] = datadict
self.adj[v][u] = datadict
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 must be given as as 2-tuples (u,v) or
3-tuples (u,v,d) where d is a dictionary containing edge
data.
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.
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.
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')
"""
# 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==3:
u,v,dd = e
elif ne==2:
u,v = e
dd = {}
else:
raise NetworkXError(\
"Edge tuple %s must be a 2-tuple or 3-tuple."%(e,))
if u not in self.adj:
self.adj[u] = {}
self.node[u] = {}
if v not in self.adj:
self.adj[v] = {}
self.node[v] = {}
datadict=self.adj[u].get(v,{})
datadict.update(attr_dict)
datadict.update(dd)
self.adj[u][v] = datadict
self.adj[v][u] = datadict
def add_weighted_edges_from(self, ebunch, **attr):
"""Add all the edges in ebunch as weighted edges with specified
weights.
Parameters
----------
ebunch : container of edges
Each edge given in the list or container will be added
to the graph. The edges must be given as 3-tuples (u,v,w)
where w is a number.
attr : keyword arguments, optional (default= no attributes)
Edge attributes to add/update for all edges.
See Also
--------
add_edge : add a single edge
add_edges_from : add multiple edges
Notes
-----
Adding the same edge twice has no effect but any edge data
will be updated when each duplicate edge is added.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_weighted_edges_from([(0,1,3.0),(1,2,7.5)])
"""
self.add_edges_from(((u,v,{'weight':d}) for u,v,d in ebunch),**attr)
def remove_edge(self, u, v):
"""Remove the edge between u and v.
Parameters
----------
u,v: nodes
Remove the edge between nodes u and v.
Raises
------
NetworkXError
If there is not an edge between u and v.
See Also
--------
remove_edges_from : remove a collection of edges
Examples
--------
>>> G = nx.Graph() # or DiGraph, etc
>>> 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
>>> e = (2,3,{'weight':7}) # an edge with attribute data
>>> G.remove_edge(*e[:2]) # select first part of edge tuple
"""
try:
del self.adj[u][v]
if u != v: # self-loop needs only one entry removed
del self.adj[v][u]
except KeyError:
raise NetworkXError("The edge %s-%s is not in the graph"%(u,v))
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) edge between u and v.
- 3-tuples (u,v,k) where k 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.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> ebunch=[(1,2),(2,3)]
>>> G.remove_edges_from(ebunch)
"""
for e in ebunch:
u,v = e[:2] # ignore edge data if present
if u in self.adj and v in self.adj[u]:
del self.adj[u][v]
if u != v: # self loop needs only one entry removed
del self.adj[v][u]
def has_edge(self, u, v):
"""Return True if the edge (u,v) is in the graph.
Parameters
----------
u,v : nodes
Nodes can be, for example, strings or numbers.
Nodes must be hashable (and not None) Python objects.
Returns
-------
edge_ind : bool
True if edge is in the graph, False otherwise.
Examples
--------
Can be called either using two nodes u,v or edge tuple (u,v)
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([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
>>> e = (0,1,{'weight':7})
>>> G.has_edge(*e[:2]) # e is a 3-tuple (u,v,data_dictionary)
True
The following syntax are all equivalent:
>>> G.has_edge(0,1)
True
>>> 1 in G[0] # though this gives KeyError if 0 not in G
True
"""
try:
return v in self.adj[u]
except KeyError:
return False
def neighbors(self, n):
"""Return a list of the nodes connected to the node n.
Parameters
----------
n : node
A node in the graph
Returns
-------
nlist : list
A list of nodes that are adjacent to n.
Raises
------
NetworkXError
If the node n is not in the graph.
Notes
-----
It is usually more convenient (and faster) to access the
adjacency dictionary as G[n]:
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge('a','b',weight=7)
>>> G['a']
{'b': {'weight': 7}}
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> G.neighbors(0)
[1]
"""
try:
return self.adj[n].keys()
except KeyError:
raise NetworkXError("The node %s is not in the graph."%(n,))
def neighbors_iter(self, n):
"""Return an iterator over all neighbors of node n.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> print [n for n in G.neighbors_iter(0)]
[1]
Notes
-----
It is faster to use the idiom "in G[0]", e.g.
>>> for n in G[0]:
... print n
1
"""
try:
return self.adj[n].iterkeys()
except KeyError:
raise NetworkXError("The node %s is not in the graph."%(n,))
def edges(self, nbunch=None, data=False):
"""Return a list of edges.
Edges are returned as tuples with optional data
in the order (node, neighbor, 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).
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.
See Also
--------
edges_iter : return an iterator over the edges
Notes
-----
Nodes in nbunch that are not in the graph will be (quietly) ignored.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> 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([0,3])
[(0, 1), (3, 2)]
>>> G.edges(0)
[(0, 1)]
"""
return list(self.edges_iter(nbunch, data))
def edges_iter(self, nbunch=None, data=False):
"""Return an iterator over the edges.
Edges are returned as tuples with optional data
in the order (node, neighbor, 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 in 3-tuple (u,v,data).
Returns
-------
edge_iter : iterator
An iterator of (u,v) or (u,v,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.
Examples
--------
>>> G = nx.Graph() # or MultiGraph, etc
>>> 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([0,3]))
[(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:
nodes_nbrs = self.adj.iteritems()
else:
nodes_nbrs=((n,self.adj[n]) for n in self.nbunch_iter(nbunch))
if data:
for n,nbrs in nodes_nbrs:
for nbr,data in nbrs.iteritems():
if nbr not in seen:
yield (n,nbr,data)
seen[n]=1
else:
for n,nbrs in nodes_nbrs:
for nbr in nbrs:
if nbr not in seen:
yield (n,nbr)
seen[n] = 1
del seen
def get_edge_data(self, u, v, 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.
Returns
-------
edge_dict : dictionary
The edge attribute dictionary.
Notes
-----
It is faster to use G[u][v].
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> G[0][1]
{}
Warning: Assigning G[u][v] corrupts the graph data structure.
But it is safe to assign attributes to that dictionary,
>>> G[0][1]['weight'] = 7
>>> G[0][1]['weight']
7
>>> G[1][0]['weight']
7
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> G.get_edge_data(0,1) # default edge data is {}
{}
>>> e = (0,1)
>>> G.get_edge_data(*e) # tuple form
{}
>>> G.get_edge_data('a','b',default=0) # edge not in graph, return 0
0
"""
try:
return self.adj[u][v]
except KeyError:
return default
def adjacency_list(self):
"""Return an adjacency list representation of the graph.
The output adjacency list is in the order of G.nodes().
For directed graphs, only outgoing adjacencies are included.
Returns
-------
adj_list : lists of lists
The adjacency structure of the graph as a list of lists.
See Also
--------
adjacency_iter
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> G.adjacency_list() # in order given by G.nodes()
[[1], [0, 2], [1, 3], [2]]
"""
return map(list,self.adj.itervalues())
def adjacency_iter(self):
"""Return an iterator of (node, adjacency dict) tuples for all nodes.
This is the fastest way to look at every edge.
For directed graphs, only outgoing adjacencies are included.
Returns
-------
adj_iter : iterator
An iterator of (node, adjacency dictionary) for all nodes in
the graph.
See Also
--------
adjacency_list
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> [(n,nbrdict) for n,nbrdict in G.adjacency_iter()]
[(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]
"""
return self.adj.iteritems()
def degree(self, nbunch=None, weighted=False):
"""Return the degree of a node or nodes.
The node degree is the number of edges adjacent to that node.
Parameters
----------
nbunch : iterable container, optional (default=all nodes)
A container of nodes. The container will be iterated
through once.
weighted : bool, optional (default=False)
If True return the sum of edge weights adjacent to the node.
Returns
-------
nd : dictionary, or number
A dictionary with nodes as keys and degree as values or
a number if a single node is specified.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> G.degree(0)
1
>>> G.degree([0,1])
{0: 1, 1: 2}
>>> G.degree([0,1]).values()
[1, 2]
"""
if nbunch in self: # return a single node
return self.degree_iter(nbunch,weighted=weighted).next()[1]
else: # return a dict
return dict(self.degree_iter(nbunch,weighted=weighted))
def degree_iter(self, nbunch=None, weighted=False):
"""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.
weighted : bool, optional (default=False)
If True return the sum of edge weights adjacent to the node.
Returns
-------
nd_iter : an iterator
The iterator returns two-tuples of (node, degree).
See Also
--------
degree
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> 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 = self.adj.iteritems()
else:
nodes_nbrs=((n,self.adj[n]) for n in self.nbunch_iter(nbunch))
if weighted:
# edge weighted graph - degree is sum of nbr edge weights
for n,nbrs in nodes_nbrs:
yield (n, sum((nbrs[nbr].get('weight',1) for nbr in nbrs)) +
(n in nbrs and nbrs[n].get('weight',1)))
else:
for n,nbrs in nodes_nbrs:
yield (n,len(nbrs)+(n in nbrs)) # return tuple (n,degree)
def clear(self):
"""Remove all nodes and edges from the graph.
This also removes the name, and all graph, node, and edge attributes.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> G.clear()
>>> G.nodes()
[]
>>> G.edges()
[]
"""
self.name = ''
self.adj.clear()
self.node.clear()
self.graph.clear()
def copy(self):
"""Return a copy of the graph.
Returns
-------
G : Graph
A copy of the graph.
See Also
--------
to_directed: return a directed copy of the graph.
Notes
-----
This makes a complete copy of the graph including all of the
node or edge attributes.
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> H = G.copy()
"""
return deepcopy(self)
def is_multigraph(self):
"""Return True if graph is a multigraph, False otherwise."""
return False
def is_directed(self):
"""Return True if graph is directed, False otherwise."""
return False
def to_directed(self):
"""Return a directed representation of the graph.
Returns
-------
G : DiGraph
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.
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.DiGraph() # or MultiDiGraph, etc
>>> G.add_path([0,1])
>>> H = G.to_directed()
>>> H.edges()
[(0, 1)]
"""
from networkx import DiGraph
G=DiGraph()
G.name=self.name
G.add_nodes_from(self)
G.add_edges_from( ((u,v,deepcopy(data))
for u,nbrs in self.adjacency_iter()
for v,data in nbrs.iteritems()) )
G.graph=deepcopy(self.graph)
G.node=deepcopy(self.node)
return G
def to_undirected(self):
"""Return an undirected copy of the graph.
Returns
-------
G : Graph/MultiGraph
A deepcopy of the graph.
See Also
--------
copy, add_edge, add_edges_from
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 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)]
>>> G2 = H.to_undirected()
>>> G2.edges()
[(0, 1)]
"""
return deepcopy(self)
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 in-place 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])
>>> print H.edges()
[(0, 1), (1, 2)]
"""
bunch =self.nbunch_iter(nbunch)
# create new graph and copy subgraph into it
H = self.__class__()
H.name = "Subgraph of (%s)"%(self.name)
# namespace shortcuts for speed
H_adj=H.adj
self_adj=self.adj
# add nodes and edges (undirected method)
for n in bunch:
Hnbrs={}
H_adj[n]=Hnbrs
for nbr,d in self_adj[n].iteritems():
if nbr in H_adj:
# add both representations of edge: n-nbr and nbr-n
Hnbrs[nbr]=d
H_adj[nbr][n]=d
# copy node and attribute dictionaries
for n in H:
H.node[n]=self.node[n]
H.graph=self.graph
return H
def nodes_with_selfloops(self):
"""Return a list of nodes with self loops.
A node with a self loop has an edge with both ends adjacent
to that node.
Returns
-------
nodelist : list
A list of nodes with self loops.
See Also
--------
selfloop_edges, number_of_selfloops
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge(1,1)
>>> G.add_edge(1,2)
>>> G.nodes_with_selfloops()
[1]
"""
return [ n for n,nbrs in self.adj.iteritems() if n in nbrs ]
def selfloop_edges(self, data=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)
Returns
-------
edgelist : list of edge tuples
A list of all selfloop edges.
See Also
--------
selfloop_nodes, number_of_selfloops
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge(1,1)
>>> G.add_edge(1,2)
>>> G.selfloop_edges()
[(1, 1)]
>>> G.selfloop_edges(data=True)
[(1, 1, {})]
"""
if data:
return [ (n,n,nbrs[n])
for n,nbrs in self.adj.iteritems() if n in nbrs ]
else:
return [ (n,n)
for n,nbrs in self.adj.iteritems() if n in nbrs ]
def number_of_selfloops(self):
"""Return the number of selfloop edges.
A selfloop edge has the same node at both ends.
Returns
-------
nloops : int
The number of selfloops.
See Also
--------
selfloop_nodes, selfloop_edges
Examples
--------
>>> G=nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge(1,1)
>>> G.add_edge(1,2)
>>> G.number_of_selfloops()
1
"""
return len(self.selfloop_edges())
def size(self, weighted=False):
"""Return the number of edges.
Parameters
----------
weighted : boolean, optional (default=False)
If True return the sum of the edge weights.
Returns
-------
nedges : int
The number of edges in the graph.
See Also
--------
number_of_edges
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> G.size()
3
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge('a','b',weight=2)
>>> G.add_edge('b','c',weight=4)
>>> G.size()
2
>>> G.size(weighted=True)
6
"""
return sum(self.degree(weighted=weighted).values())/2
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
>>> G.add_path([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()
if v in self.adj[u]:
return 1
else:
return 0
def add_star(self, nlist, **attr):
"""Add a star.
The first node in nlist is the middle of the star. It is connected
to all other nodes in nlist.
Parameters
----------
nlist : list
A list of nodes.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to every edge in star.
See Also
--------
add_path, add_cycle
Examples
--------
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_star([0,1,2,3])
>>> G.add_star([10,11,12],weight=2)
"""
v=nlist[0]
edges=((v,n) for n in nlist[1:])
self.add_edges_from(edges, **attr)
def add_path(self, nlist, **attr):
"""Add a path.
Parameters
----------
nlist : list
A list of nodes. A path will be constructed from
the nodes (in order) and added to the graph.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to every edge in path.
See Also
--------
add_star, add_cycle
Examples
--------
>>> G=nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> G.add_path([10,11,12],weight=7)
"""
edges=zip(nlist[:-1],nlist[1:])
self.add_edges_from(edges, **attr)
def add_cycle(self, nlist, **attr):
"""Add a cycle.
Parameters
----------
nlist : list
A list of nodes. A cycle will be constructed from
the nodes (in order) and added to the graph.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to every edge in cycle.
See Also
--------
add_path, add_star
Examples
--------
>>> G=nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_cycle([0,1,2,3])
>>> G.add_cycle([10,11,12],weight=7)
"""
edges=zip(nlist,nlist[1:]+[nlist[0]])
self.add_edges_from(edges, **attr)
def nbunch_iter(self, nbunch=None):
"""Return an iterator of nodes contained in nbunch that are
also in the graph.
The nodes in nbunch are checked for membership in the graph
and if not are silently ignored.
Parameters
----------
nbunch : iterable container, optional (default=all nodes)
A container of nodes. The container will be iterated
through once.
Returns
-------
niter : iterator
An iterator over nodes in nbunch that are also in the graph.
If nbunch is None, iterate over all nodes in the graph.
Raises
------
NetworkXError
If nbunch is not a node or or sequence of nodes.
If a node in nbunch is not hashable.
See Also
--------
Graph.__iter__
Notes
-----
When nbunch is an iterator, the returned iterator yields values
directly from nbunch, becoming exhausted when nbunch is exhausted.
To test whether nbunch is a single node, one can use
"if nbunch in self:", even after processing with this routine.
If nbunch is not a node or a (possibly empty) sequence/iterator
or None, a NetworkXError is raised. Also, if any object in
nbunch is not hashable, a NetworkXError is raised.
"""
if nbunch is None: # include all nodes via iterator
bunch=self.adj.iterkeys()
elif nbunch in self: # if nbunch is a single node
bunch=[nbunch].__iter__()
else: # if nbunch is a sequence of nodes
def bunch_iter(nlist,adj):
try:
for n in nlist:
if n in adj:
yield n
except TypeError,e:
message=e.args[0]
print message
# capture error for non-sequence/iterator nbunch.
if 'iter' in message:
raise NetworkXError(
"nbunch is not a node or a sequence of nodes.")
# capture error for unhashable node.
elif 'hashable' in message:
raise NetworkXError(
"Node %s in the sequence nbunch is not a valid node."%n)
else: raise
bunch=bunch_iter(nbunch,self.adj)
return bunch
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