# Copyright (C) 2004-2019 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
#
# Author: Aric Hagberg (hagberg@lanl.gov),
# Pieter Swart (swart@lanl.gov),
# Dan Schult(dschult@colgate.edu)
"""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.
"""
import warnings
from copy import deepcopy
from collections.abc import Mapping
import networkx as nx
from networkx.classes.coreviews import AtlasView, AdjacencyView
from networkx.classes.reportviews import NodeView, EdgeView, DegreeView
from networkx.exception import NetworkXError
import networkx.convert as convert
from networkx.utils import pairwise
[docs]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. By convention `None` is not used as a node.
Edges are represented as links between nodes with optional
key/value attributes.
Parameters
----------
incoming_graph_data : input graph (optional, default: None)
Data to initialize graph. If 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
--------
DiGraph
MultiGraph
MultiDiGraph
OrderedGraph
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.nodes
>>> G.add_node(1, time='5pm')
>>> G.add_nodes_from([3], time='2pm')
>>> G.nodes[1]
{'time': '5pm'}
>>> G.nodes[1]['room'] = 714 # node must exist already to use G.nodes
>>> del G.nodes[1]['room'] # remove attribute
>>> list(G.nodes(data=True))
[(1, {'time': '5pm'}), (3, {'time': '2pm'})]
Add edge attributes using add_edge(), add_edges_from(), subscript
notation, or G.edges.
>>> 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.edges[1, 2]['weight'] = 4
Warning: we protect the graph data structure by making `G.edges` a
read-only dict-like structure. However, you can assign to attributes
in e.g. `G.edges[1, 2]`. Thus, use 2 sets of brackets to add/change
data attributes: `G.edges[1, 2]['weight'] = 4`
(For multigraphs: `MG.edges[u, v, key][name] = value`).
**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
Often the best way to traverse all edges of a graph is via the neighbors.
The neighbors are reported as an adjacency-dict `G.adj` or `G.adjacency()`
>>> for n, nbrsdict in G.adjacency():
... for nbr, eattr in nbrsdict.items():
... if 'weight' in eattr:
... # Do something useful with the edges
... pass
But the edges() method is often more convenient:
>>> for u, v, weight in G.edges.data('weight'):
... if weight is not None:
... # Do something useful with the edges
... pass
**Reporting:**
Simple graph information is obtained using object-attributes and methods.
Reporting typically provides views instead of containers to reduce memory
usage. The views update as the graph is updated similarly to dict-views.
The objects `nodes, `edges` and `adj` provide access to data attributes
via lookup (e.g. `nodes[n], `edges[u, v]`, `adj[u][v]`) and iteration
(e.g. `nodes.items()`, `nodes.data('color')`,
`nodes.data('color', default='blue')` and similarly for `edges`)
Views exist for `nodes`, `edges`, `neighbors()`/`adj` and `degree`.
For details on these and other miscellaneous methods, see below.
**Subclasses (Advanced):**
The Graph class uses a 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 data keyed by neighbor. The inner dict (edge_attr_dict) represents
the edge data and holds edge attribute values keyed by attribute names.
Each of these three dicts can be replaced in a subclass 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, node_attr_dict_factory, adjlist_inner_dict_factory,
adjlist_outer_dict_factory, edge_attr_dict_factory and graph_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
node_attr_dict_factory: function, (default: dict)
Factory function to be used to create the node attribute
dict which holds attribute values keyed by attribute name.
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 edge data keyed by neighbor.
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 attribute values keyed by attribute name.
It should require no arguments and return a dict-like object.
graph_attr_dict_factory : function, (default: dict)
Factory function to be used to create the graph attribute
dict which holds attribute values keyed by attribute name.
It should require no arguments and return a dict-like object.
Typically, if your extension doesn't impact the data structure all
methods will inherit without issue except: `to_directed/to_undirected`.
By default these methods create a DiGraph/Graph class and you probably
want them to create your extension of a DiGraph/Graph. To facilitate
this we define two class variables that you can set in your subclass.
to_directed_class : callable, (default: DiGraph or MultiDiGraph)
Class to create a new graph structure in the `to_directed` method.
If `None`, a NetworkX class (DiGraph or MultiDiGraph) is used.
to_undirected_class : callable, (default: Graph or MultiGraph)
Class to create a new graph structure in the `to_undirected` method.
If `None`, a NetworkX class (Graph or MultiGraph) is used.
Examples
--------
Create a low memory graph class that effectively disallows edge
attributes by using a single attribute dict for all edges.
This reduces the memory used, but you lose edge attributes.
>>> class ThinGraph(nx.Graph):
... all_edge_dict = {'weight': 1}
... def single_edge_dict(self):
... return self.all_edge_dict
... edge_attr_dict_factory = single_edge_dict
>>> G = ThinGraph()
>>> G.add_edge(2, 1)
>>> G[2][1]
{'weight': 1}
>>> G.add_edge(2, 2)
>>> G[2][1] is G[2][2]
True
Please see :mod:`~networkx.classes.ordered` for more examples of
creating graph subclasses by overwriting the base class `dict` with
a dictionary-like object.
"""
node_dict_factory = dict
node_attr_dict_factory = dict
adjlist_outer_dict_factory = dict
adjlist_inner_dict_factory = dict
edge_attr_dict_factory = dict
graph_attr_dict_factory = dict
def to_directed_class(self):
"""Returns the class to use for empty directed copies.
If you subclass the base classes, use this to designate
what directed class to use for `to_directed()` copies.
"""
return nx.DiGraph
def to_undirected_class(self):
"""Returns the class to use for empty undirected copies.
If you subclass the base classes, use this to designate
what directed class to use for `to_directed()` copies.
"""
return Graph
[docs] def __init__(self, incoming_graph_data=None, **attr):
"""Initialize a graph with edges, name, or graph attributes.
Parameters
----------
incoming_graph_data : input graph (optional, default: None)
Data to initialize graph. If 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
--------
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_attr_dict_factory = self.graph_attr_dict_factory
self.node_dict_factory = self.node_dict_factory
self.node_attr_dict_factory = self.node_attr_dict_factory
self.adjlist_outer_dict_factory = self.adjlist_outer_dict_factory
self.adjlist_inner_dict_factory = self.adjlist_inner_dict_factory
self.edge_attr_dict_factory = self.edge_attr_dict_factory
self.graph = self.graph_attr_dict_factory() # dictionary for graph attributes
self._node = self.node_dict_factory() # empty node attribute dict
self._adj = self.adjlist_outer_dict_factory() # empty adjacency dict
# attempt to load graph with data
if incoming_graph_data is not None:
convert.to_networkx_graph(incoming_graph_data, create_using=self)
# load graph attributes (must be after convert)
self.graph.update(attr)
@property
def adj(self):
"""Graph adjacency object holding the neighbors of each node.
This object is a read-only dict-like structure with node keys
and neighbor-dict values. The neighbor-dict is keyed by neighbor
to the edge-data-dict. So `G.adj[3][2]['color'] = 'blue'` sets
the color of the edge `(3, 2)` to `"blue"`.
Iterating over G.adj behaves like a dict. Useful idioms include
`for nbr, datadict in G.adj[n].items():`.
The neighbor information is also provided by subscripting the graph.
So `for nbr, foovalue in G[node].data('foo', default=1):` works.
For directed graphs, `G.adj` holds outgoing (successor) info.
"""
return AdjacencyView(self._adj)
@property
def name(self):
"""String identifier of the graph.
This graph attribute appears in the attribute dict G.graph
keyed by the string `"name"`. as well as an attribute (technically
a property) `G.name`. This is entirely user controlled.
"""
return self.graph.get('name', '')
@name.setter
def name(self, s):
self.graph['name'] = s
def __str__(self):
"""Returns the graph name.
Returns
-------
name : string
The name of the graph.
Examples
--------
>>> G = nx.Graph(name='foo')
>>> str(G)
'foo'
"""
return self.name
[docs] def __iter__(self):
"""Iterate over the nodes. Use: 'for n in G'.
Returns
-------
niter : iterator
An iterator over all nodes in the graph.
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> [n for n in G]
[0, 1, 2, 3]
>>> list(G)
[0, 1, 2, 3]
"""
return iter(self._node)
[docs] def __contains__(self, n):
"""Returns True if n is a node, False otherwise. Use: 'n in G'.
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> 1 in G
True
"""
try:
return n in self._node
except TypeError:
return False
[docs] def __len__(self):
"""Returns the number of nodes in the graph. Use: 'len(G)'.
Returns
-------
nnodes : int
The number of nodes in the graph.
See Also
--------
number_of_nodes, order which are identical
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> len(G)
4
"""
return len(self._node)
[docs] def __getitem__(self, n):
"""Returns a dict of neighbors of node n. Use: '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 the same as G.adj[n] and similar to G.neighbors(n)
(which is an iterator over G.adj[n])
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G[0]
AtlasView({1: {}})
"""
return self.adj[n]
[docs] def add_node(self, node_for_adding, **attr):
"""Add a single node `node_for_adding` and update node attributes.
Parameters
----------
node_for_adding : node
A node can be any hashable Python object except None.
attr : keyword arguments, optional
Set or change node 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.
"""
if node_for_adding not in self._node:
self._adj[node_for_adding] = self.adjlist_inner_dict_factory()
attr_dict = self._node[node_for_adding] = self.node_attr_dict_factory()
attr_dict.update(attr)
else: # update attr even if node already exists
self._node[node_for_adding].update(attr)
[docs] def add_nodes_from(self, nodes_for_adding, **attr):
"""Add multiple nodes.
Parameters
----------
nodes_for_adding : 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 via keyword arguments.
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(), key=str)
[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.nodes[1]['size']
11
>>> H = nx.Graph()
>>> H.add_nodes_from(G.nodes(data=True))
>>> H.nodes[1]['size']
11
"""
for n in nodes_for_adding:
# keep all this inside try/except because
# CPython throws TypeError on n not in self._node,
# while pre-2.7.5 ironpython throws on self._adj[n]
try:
if n not in self._node:
self._adj[n] = self.adjlist_inner_dict_factory()
attr_dict = self._node[n] = self.node_attr_dict_factory()
attr_dict.update(attr)
else:
self._node[n].update(attr)
except TypeError:
nn, ndict = n
if nn not in self._node:
self._adj[nn] = self.adjlist_inner_dict_factory()
newdict = attr.copy()
newdict.update(ndict)
attr_dict = self._node[nn] = self.node_attr_dict_factory()
attr_dict.update(newdict)
else:
olddict = self._node[nn]
olddict.update(attr)
olddict.update(ndict)
[docs] 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.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> list(G.edges)
[(0, 1), (1, 2)]
>>> G.remove_node(1)
>>> list(G.edges)
[]
"""
adj = self._adj
try:
nbrs = list(adj[n]) # list handles self-loops (allows mutation)
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
[docs] 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.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = list(G.nodes)
>>> e
[0, 1, 2]
>>> G.remove_nodes_from(e)
>>> list(G.nodes)
[]
"""
adj = self._adj
for n in nodes:
try:
del self._node[n]
for u in list(adj[n]): # list handles self-loops
del adj[u][n] # (allows mutation of dict in loop)
del adj[n]
except KeyError:
pass
@property
def nodes(self):
"""A NodeView of the Graph as G.nodes or G.nodes().
Can be used as `G.nodes` for data lookup and for set-like operations.
Can also be used as `G.nodes(data='color', default=None)` to return a
NodeDataView which reports specific node data but no set operations.
It presents a dict-like interface as well with `G.nodes.items()`
iterating over `(node, nodedata)` 2-tuples and `G.nodes[3]['foo']`
providing the value of the `foo` attribute for node `3`. In addition,
a view `G.nodes.data('foo')` provides a dict-like interface to the
`foo` attribute of each node. `G.nodes.data('foo', default=1)`
provides a default for nodes that do not have attribute `foo`.
Parameters
----------
data : string or bool, optional (default=False)
The node attribute returned in 2-tuple (n, ddict[data]).
If True, return entire node attribute dict as (n, ddict).
If False, return just the nodes n.
default : value, optional (default=None)
Value used for nodes that don't have the requested attribute.
Only relevant if data is not True or False.
Returns
-------
NodeView
Allows set-like operations over the nodes as well as node
attribute dict lookup and calling to get a NodeDataView.
A NodeDataView iterates over `(n, data)` and has no set operations.
A NodeView iterates over `n` and includes set operations.
When called, if data is False, an iterator over nodes.
Otherwise an iterator of 2-tuples (node, attribute value)
where the attribute is specified in `data`.
If data is True then the attribute becomes the
entire data dictionary.
Notes
-----
If your node data is not needed, it is simpler and equivalent
to use the expression ``for n in G``, or ``list(G)``.
Examples
--------
There are two simple ways of getting a list of all nodes in the graph:
>>> G = nx.path_graph(3)
>>> list(G.nodes)
[0, 1, 2]
>>> list(G)
[0, 1, 2]
To get the node data along with the nodes:
>>> G.add_node(1, time='5pm')
>>> G.nodes[0]['foo'] = 'bar'
>>> list(G.nodes(data=True))
[(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]
>>> list(G.nodes.data())
[(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]
>>> list(G.nodes(data='foo'))
[(0, 'bar'), (1, None), (2, None)]
>>> list(G.nodes.data('foo'))
[(0, 'bar'), (1, None), (2, None)]
>>> list(G.nodes(data='time'))
[(0, None), (1, '5pm'), (2, None)]
>>> list(G.nodes.data('time'))
[(0, None), (1, '5pm'), (2, None)]
>>> list(G.nodes(data='time', default='Not Available'))
[(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]
>>> list(G.nodes.data('time', default='Not Available'))
[(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]
If some of your nodes have an attribute and the rest are assumed
to have a default attribute value you can create a dictionary
from node/attribute pairs using the `default` keyword argument
to guarantee the value is never None::
>>> G = nx.Graph()
>>> G.add_node(0)
>>> G.add_node(1, weight=2)
>>> G.add_node(2, weight=3)
>>> dict(G.nodes(data='weight', default=1))
{0: 1, 1: 2, 2: 3}
"""
nodes = NodeView(self)
# Lazy View creation: overload the (class) property on the instance
# Then future G.nodes use the existing View
# setattr doesn't work because attribute already exists
self.__dict__['nodes'] = nodes
return nodes
[docs] def number_of_nodes(self):
"""Returns 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.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.number_of_nodes()
3
"""
return len(self._node)
[docs] def order(self):
"""Returns 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
Examples
--------
>>> G = nx.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.order()
3
"""
return len(self._node)
[docs] def has_node(self, n):
"""Returns True if the graph contains the node n.
Identical to `n in G`
Parameters
----------
n : node
Examples
--------
>>> G = nx.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_node(0)
True
It is more readable and simpler to use
>>> 0 in G
True
"""
try:
return n in self._node
except TypeError:
return False
[docs] def add_edge(self, u_of_edge, v_of_edge, **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.
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.
Many NetworkX algorithms designed for weighted graphs use
an edge attribute (by default `weight`) to hold a numerical value.
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)
For non-string attribute keys, use subscript notation.
>>> G.add_edge(1, 2)
>>> G[1][2].update({0: 5})
>>> G.edges[1, 2].update({0: 5})
"""
u, v = u_of_edge, v_of_edge
# add nodes
if u not in self._node:
self._adj[u] = self.adjlist_inner_dict_factory()
self._node[u] = self.node_attr_dict_factory()
if v not in self._node:
self._adj[v] = self.adjlist_inner_dict_factory()
self._node[v] = self.node_attr_dict_factory()
# add the edge
datadict = self._adj[u].get(v, self.edge_attr_dict_factory())
datadict.update(attr)
self._adj[u][v] = datadict
self._adj[v][u] = datadict
[docs] def add_edges_from(self, ebunch_to_add, **attr):
"""Add all the edges in ebunch_to_add.
Parameters
----------
ebunch_to_add : 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 : 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.
Edge attributes specified in an ebunch take precedence over
attributes specified via keyword arguments.
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')
"""
for e in ebunch_to_add:
ne = len(e)
if ne == 3:
u, v, dd = e
elif ne == 2:
u, v = e
dd = {} # doesn't need edge_attr_dict_factory
else:
raise NetworkXError(
"Edge tuple %s must be a 2-tuple or 3-tuple." % (e,))
if u not in self._node:
self._adj[u] = self.adjlist_inner_dict_factory()
self._node[u] = self.node_attr_dict_factory()
if v not in self._node:
self._adj[v] = self.adjlist_inner_dict_factory()
self._node[v] = self.node_attr_dict_factory()
datadict = self._adj[u].get(v, self.edge_attr_dict_factory())
datadict.update(attr)
datadict.update(dd)
self._adj[u][v] = datadict
self._adj[v][u] = datadict
[docs] def add_weighted_edges_from(self, ebunch_to_add, weight='weight', **attr):
"""Add weighted edges in `ebunch_to_add` with specified weight attr
Parameters
----------
ebunch_to_add : 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.
weight : string, optional (default= 'weight')
The attribute name for the edge weights to be added.
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 for Graph/DiGraph simply updates
the edge data. For MultiGraph/MultiDiGraph, duplicate edges
are stored.
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_to_add),
**attr)
[docs] 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.path_graph(4) # or DiGraph, etc
>>> 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))
[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) 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.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> ebunch=[(1, 2), (2, 3)]
>>> G.remove_edges_from(ebunch)
"""
adj = self._adj
for e in ebunch:
u, v = e[:2] # ignore edge data if present
if u in adj and v in adj[u]:
del adj[u][v]
if u != v: # self loop needs only one entry removed
del adj[v][u]
[docs] def update(self, edges=None, nodes=None):
"""Update the graph using nodes/edges/graphs as input.
Like dict.update, this method takes a graph as input, adding the
graph's nodes and edges to this graph. It can also take two inputs:
edges and nodes. Finally it can take either edges or nodes.
To specify only nodes the keyword `nodes` must be used.
The collections of edges and nodes are treated similarly to
the add_edges_from/add_nodes_from methods. When iterated, they
should yield 2-tuples (u, v) or 3-tuples (u, v, datadict).
Parameters
----------
edges : Graph object, collection of edges, or None
The first parameter can be a graph or some edges. If it has
attributes `nodes` and `edges`, then it is taken to be a
Graph-like object and those attributes are used as collections
of nodes and edges to be added to the graph.
If the first parameter does not have those attributes, it is
treated as a collection of edges and added to the graph.
If the first argument is None, no edges are added.
nodes : collection of nodes, or None
The second parameter is treated as a collection of nodes
to be added to the graph unless it is None.
If `edges is None` and `nodes is None` an exception is raised.
If the first parameter is a Graph, then `nodes` is ignored.
Examples
--------
>>> G = nx.path_graph(5)
>>> G.update(nx.complete_graph(range(4,10)))
>>> from itertools import combinations
>>> edges = ((u, v, {'power': u * v})
... for u, v in combinations(range(10, 20), 2)
... if u * v < 225)
>>> nodes = [1000] # for singleton, use a container
>>> G.update(edges, nodes)
Notes
-----
It you want to update the graph using an adjacency structure
it is straightforward to obtain the edges/nodes from adjacency.
The following examples provide common cases, your adjacency may
be slightly different and require tweaks of these examples.
>>> # dict-of-set/list/tuple
>>> adj = {1: {2, 3}, 2: {1, 3}, 3: {1, 2}}
>>> e = [(u, v) for u, nbrs in adj.items() for v in nbrs]
>>> G.update(edges=e, nodes=adj)
>>> DG = nx.DiGraph()
>>> # dict-of-dict-of-attribute
>>> adj = {1: {2: 1.3, 3: 0.7}, 2: {1: 1.4}, 3: {1: 0.7}}
>>> e = [(u, v, {'weight': d}) for u, nbrs in adj.items()
... for v, d in nbrs.items()]
>>> DG.update(edges=e, nodes=adj)
>>> # dict-of-dict-of-dict
>>> adj = {1: {2: {'weight': 1.3}, 3: {'color': 0.7, 'weight':1.2}}}
>>> e = [(u, v, {'weight': d}) for u, nbrs in adj.items()
... for v, d in nbrs.items()]
>>> DG.update(edges=e, nodes=adj)
>>> # predecessor adjacency (dict-of-set)
>>> pred = {1: {2, 3}, 2: {3}, 3: {3}}
>>> e = [(v, u) for u, nbrs in pred.items() for v in nbrs]
>>> # MultiGraph dict-of-dict-of-dict-of-attribute
>>> MDG = nx.MultiDiGraph()
>>> adj = {1: {2: {0: {'weight': 1.3}, 1: {'weight': 1.2}}},
... 3: {2: {0: {'weight': 0.7}}}}
>>> e = [(u, v, ekey, d) for u, nbrs in adj.items()
... for v, keydict in nbrs.items()
... for ekey, d in keydict.items()]
>>> MDG.update(edges=e)
See Also
--------
add_edges_from: add multiple edges to a graph
add_nodes_from: add multiple nodes to a graph
"""
if edges is not None:
if nodes is not None:
self.add_nodes_from(nodes)
self.add_edges_from(edges)
else:
# check if edges is a Graph object
try:
graph_nodes = edges.nodes
graph_edges = edges.edges
except AttributeError:
# edge not Graph-like
self.add_edges_from(edges)
else: # edges is Graph-like
self.add_nodes_from(graph_nodes.data())
self.add_edges_from(graph_edges.data())
self.graph.update(edges.graph)
elif nodes is not None:
self.add_nodes_from(nodes)
else:
raise NetworkXError("update needs nodes or edges input")
[docs] def has_edge(self, u, v):
"""Returns True if the edge (u, v) is in the graph.
This is the same as `v in G[u]` without KeyError exceptions.
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
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> 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 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
[docs] def neighbors(self, n):
"""Returns an iterator over all neighbors of node n.
This is identical to `iter(G[n])`
Parameters
----------
n : node
A node in the graph
Returns
-------
neighbors : iterator
An iterator over all neighbors of node n
Raises
------
NetworkXError
If the node n is not in the graph.
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> [n for n in G.neighbors(0)]
[1]
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']
AtlasView({'b': {'weight': 7}})
>>> G = nx.path_graph(4)
>>> [n for n in G[0]]
[1]
"""
try:
return iter(self._adj[n])
except KeyError:
raise NetworkXError("The node %s is not in the graph." % (n,))
@property
def edges(self):
"""An EdgeView of the Graph as G.edges or G.edges().
edges(self, nbunch=None, data=False, default=None)
The EdgeView provides set-like operations on the edge-tuples
as well as edge attribute lookup. When called, it also provides
an EdgeDataView object which allows control of access to edge
attributes (but does not provide set-like operations).
Hence, `G.edges[u, v]['color']` provides the value of the color
attribute for edge `(u, v)` while
`for (u, v, c) in G.edges.data('color', default='red'):`
iterates through all the edges yielding the color attribute
with default `'red'` if no color attribute exists.
Parameters
----------
nbunch : single node, container, or all nodes (default= all nodes)
The view will only report edges incident to these nodes.
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 don't have the requested attribute.
Only relevant if data is not True or False.
Returns
-------
edges : EdgeView
A view of edge attributes, usually it iterates over (u, v)
or (u, v, d) tuples of edges, but can also be used for
attribute lookup as `edges[u, v]['foo']`.
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.path_graph(3) # or MultiGraph, etc
>>> G.add_edge(2, 3, weight=5)
>>> [e for e in G.edges]
[(0, 1), (1, 2), (2, 3)]
>>> G.edges.data() # default data is {} (empty dict)
EdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
>>> G.edges.data('weight', default=1)
EdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
>>> G.edges([0, 3]) # only edges incident to these nodes
EdgeDataView([(0, 1), (3, 2)])
>>> G.edges(0) # only edges incident to a single node (use G.adj[0]?)
EdgeDataView([(0, 1)])
"""
return EdgeView(self)
[docs] def get_edge_data(self, u, v, default=None):
"""Returns the attribute dictionary associated with edge (u, v).
This is identical to `G[u][v]` except the default is returned
instead of an exception if the edge doesn't exist.
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.
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G[0][1]
{}
Warning: Assigning to `G[u][v]` is not permitted.
But it is safe to assign attributes `G[u][v]['foo']`
>>> G[0][1]['weight'] = 7
>>> G[0][1]['weight']
7
>>> G[1][0]['weight']
7
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> 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
[docs] def adjacency(self):
"""Returns an iterator over (node, adjacency dict) tuples for all nodes.
For directed graphs, only outgoing neighbors/adjacencies are included.
Returns
-------
adj_iter : iterator
An iterator over (node, adjacency dictionary) for all nodes in
the graph.
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> [(n, nbrdict) for n, nbrdict in G.adjacency()]
[(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]
"""
return iter(self._adj.items())
@property
def degree(self):
"""A DegreeView for the Graph as G.degree or G.degree().
The node degree is the number of edges adjacent to the node.
The weighted node degree is the sum of the edge weights for
edges incident to that node.
This object provides an iterator for (node, degree) as well as
lookup for the degree for a single node.
Parameters
----------
nbunch : single node, container, or all nodes (default= all nodes)
The view will only report edges incident to these nodes.
weight : string or None, optional (default=None)
The name of an 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
OR if multiple nodes are requested
nd_view : A DegreeView object capable of iterating (node, degree) pairs
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.degree[0] # node 0 has degree 1
1
>>> list(G.degree([0, 1, 2]))
[(0, 1), (1, 2), (2, 2)]
"""
return DegreeView(self)
[docs] 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.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear()
>>> list(G.nodes)
[]
>>> list(G.edges)
[]
"""
self._adj.clear()
self._node.clear()
self.graph.clear()
def is_multigraph(self):
"""Returns True if graph is a multigraph, False otherwise."""
return False
def is_directed(self):
"""Returns True if graph is directed, False otherwise."""
return False
[docs] def copy(self, as_view=False):
"""Returns a copy of the graph.
The copy method by default returns an independent shallow copy
of the graph and attributes. That is, if an attribute is a
container, that container is shared by the original an the copy.
Use Python's `copy.deepcopy` for new containers.
If `as_view` is True then a view is returned instead of a copy.
Notes
-----
All copies reproduce the graph structure, but data attributes
may be handled in different ways. There are four types of copies
of a graph that people might want.
Deepcopy -- A "deepcopy" copies the graph structure as well as
all data attributes and any objects they might contain.
The entire graph object is new so that changes in the copy
do not affect the original object. (see Python's copy.deepcopy)
Data Reference (Shallow) -- For a shallow copy the graph structure
is copied but the edge, node and graph attribute dicts are
references to those in the original graph. This saves
time and memory but could cause confusion if you change an attribute
in one graph and it changes the attribute in the other.
NetworkX does not provide this level of shallow copy.
Independent Shallow -- This copy creates new independent attribute
dicts and then does a shallow copy of the attributes. That is, any
attributes that are containers are shared between the new graph
and the original. This is exactly what `dict.copy()` provides.
You can obtain this style copy using:
>>> G = nx.path_graph(5)
>>> H = G.copy()
>>> H = G.copy(as_view=False)
>>> H = nx.Graph(G)
>>> H = G.__class__(G)
Fresh Data -- For fresh data, the graph structure is copied while
new empty data attribute dicts are created. The resulting graph
is independent of the original and it has no edge, node or graph
attributes. Fresh copies are not enabled. Instead use:
>>> H = G.__class__()
>>> H.add_nodes_from(G)
>>> H.add_edges_from(G.edges)
View -- Inspired by dict-views, graph-views act like read-only
versions of the original graph, providing a copy of the original
structure without requiring any memory for copying the information.
See the Python copy module for more information on shallow
and deep copies, https://docs.python.org/2/library/copy.html.
Parameters
----------
as_view : bool, optional (default=False)
If True, the returned graph-view provides a read-only view
of the original graph without actually copying any data.
Returns
-------
G : Graph
A copy of the graph.
See Also
--------
to_directed: return a directed copy of the graph.
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.copy()
"""
if as_view is True:
return nx.graphviews.generic_graph_view(self)
G = self.__class__()
G.graph.update(self.graph)
G.add_nodes_from((n, d.copy()) for n, d in self._node.items())
G.add_edges_from((u, v, datadict.copy())
for u, nbrs in self._adj.items()
for v, datadict in nbrs.items())
return G
[docs] def to_directed(self, as_view=False):
"""Returns 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, https://docs.python.org/2/library/copy.html.
Warning: If you have subclassed Graph to use dict-like objects
in the data structure, those changes do not transfer to the
DiGraph 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)]
"""
graph_class = self.to_directed_class()
if as_view is True:
return nx.graphviews.generic_graph_view(self, graph_class)
# deepcopy when not a view
G = graph_class()
G.graph.update(deepcopy(self.graph))
G.add_nodes_from((n, deepcopy(d)) for n, d in self._node.items())
G.add_edges_from((u, v, deepcopy(data))
for u, nbrs in self._adj.items()
for v, data in nbrs.items())
return G
[docs] def to_undirected(self, as_view=False):
"""Returns an undirected copy of the graph.
Parameters
----------
as_view : bool (optional, default=False)
If True return a view of the original undirected graph.
Returns
-------
G : Graph/MultiGraph
A deepcopy of the graph.
See Also
--------
Graph, 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 = nx.DiGraph(D)` which returns a
shallow copy of the data.
See the Python copy module for more information on shallow
and deep copies, https://docs.python.org/2/library/copy.html.
Warning: If you have subclassed DiGraph to use dict-like objects
in the data structure, those changes do not transfer to the
Graph created by this method.
Examples
--------
>>> G = nx.path_graph(2) # or MultiGraph, etc
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]
>>> G2 = H.to_undirected()
>>> list(G2.edges)
[(0, 1)]
"""
graph_class = self.to_undirected_class()
if as_view is True:
return nx.graphviews.generic_graph_view(self, graph_class)
# deepcopy when not a view
G = graph_class()
G.graph.update(deepcopy(self.graph))
G.add_nodes_from((n, deepcopy(d)) for n, d in self._node.items())
G.add_edges_from((u, v, deepcopy(d))
for u, nbrs in self._adj.items()
for v, d in nbrs.items())
return G
[docs] def subgraph(self, nodes):
"""Returns a SubGraph view of the subgraph induced on `nodes`.
The induced subgraph of the graph contains the nodes in `nodes`
and the edges between those nodes.
Parameters
----------
nodes : list, iterable
A container of nodes which will be iterated through once.
Returns
-------
G : SubGraph View
A subgraph view of the graph. The graph structure cannot be
changed but node/edge attributes can and are shared with the
original graph.
Notes
-----
The graph, edge and node attributes are shared with the original graph.
Changes to the graph structure is ruled out by the view, but changes
to attributes are reflected in the original graph.
To create a subgraph with its own copy of the edge/node attributes use:
G.subgraph(nodes).copy()
For an inplace reduction of a graph to a subgraph you can remove nodes:
G.remove_nodes_from([n for n in G if n not in set(nodes)])
Subgraph views are sometimes NOT what you want. In most cases where
you want to do more than simply look at the induced edges, it makes
more sense to just create the subgraph as its own graph with code like:
::
# Create a subgraph SG based on a (possibly multigraph) G
SG = G.__class__()
SG.add_nodes_from((n, G.nodes[n]) for n in largest_wcc)
if SG.is_multigraph:
SG.add_edges_from((n, nbr, key, d)
for n, nbrs in G.adj.items() if n in largest_wcc
for nbr, keydict in nbrs.items() if nbr in largest_wcc
for key, d in keydict.items())
else:
SG.add_edges_from((n, nbr, d)
for n, nbrs in G.adj.items() if n in largest_wcc
for nbr, d in nbrs.items() if nbr in largest_wcc)
SG.graph.update(G.graph)
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.subgraph([0, 1, 2])
>>> list(H.edges)
[(0, 1), (1, 2)]
"""
induced_nodes = nx.filters.show_nodes(self.nbunch_iter(nodes))
# if already a subgraph, don't make a chain
subgraph = nx.graphviews.subgraph_view
if hasattr(self, '_NODE_OK'):
return subgraph(self._graph, induced_nodes, self._EDGE_OK)
return subgraph(self, induced_nodes)
[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
view are references to the corresponding attributes in the original
graph. The view is read-only.
To create a full graph version of the subgraph with its own copy
of the edge or node attributes, use::
>>> G.edge_subgraph(edges).copy() # doctest: +SKIP
Examples
--------
>>> G = nx.path_graph(5)
>>> H = G.edge_subgraph([(0, 1), (3, 4)])
>>> list(H.nodes)
[0, 1, 3, 4]
>>> list(H.edges)
[(0, 1), (3, 4)]
"""
return nx.edge_subgraph(self, edges)
[docs] def size(self, weight=None):
"""Returns the number of edges or total of all edge weights.
Parameters
----------
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.
Returns
-------
size : numeric
The number of edges or
(if weight keyword is provided) the total weight sum.
If weight is None, returns an int. Otherwise a float
(or more general numeric if the weights are more general).
See Also
--------
number_of_edges
Examples
--------
>>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> 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(weight='weight')
6.0
"""
s = sum(d for v, d in self.degree(weight=weight))
# If `weight` is None, the sum of the degrees is guaranteed to be
# even, so we can perform integer division and hence return an
# integer. Otherwise, the sum of the weighted degrees is not
# guaranteed to be an integer, so we perform "real" division.
return s // 2 if weight is None else s / 2
[docs] def number_of_edges(self, u=None, v=None):
"""Returns 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. If
the graph is directed, this only returns the number of edges
from `u` to `v`.
See Also
--------
size
Examples
--------
For undirected graphs, this method counts the total number of
edges in the graph:
>>> G = nx.path_graph(4)
>>> G.number_of_edges()
3
If you specify two nodes, this counts the total number of edges
joining the two nodes:
>>> G.number_of_edges(0, 1)
1
For directed graphs, this method can count the total number of
directed edges from `u` to `v`:
>>> G = nx.DiGraph()
>>> G.add_edge(0, 1)
>>> G.add_edge(1, 0)
>>> G.number_of_edges(0, 1)
1
"""
if u is None:
return int(self.size())
if v in self._adj[u]:
return 1
return 0
[docs] def nbunch_iter(self, nbunch=None):
"""Returns an iterator over 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 : single node, container, or all nodes (default= all nodes)
The view will only report edges incident to these nodes.
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 :exc:`NetworkXError` is raised. Also, if any object in
nbunch is not hashable, a :exc:`NetworkXError` is raised.
"""
if nbunch is None: # include all nodes via iterator
bunch = iter(self._adj)
elif nbunch in self: # if nbunch is a single node
bunch = iter([nbunch])
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 as e:
message = e.args[0]
# capture error for non-sequence/iterator nbunch.
if 'iter' in message:
msg = "nbunch is not a node or a sequence of nodes."
raise NetworkXError(msg)
# capture error for unhashable node.
elif 'hashable' in message:
msg = "Node {} in sequence nbunch is not a valid node."
raise NetworkXError(msg.format(n))
else:
raise
bunch = bunch_iter(nbunch, self._adj)
return bunch