Warning

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

# Source code for networkx.algorithms.components.connected

# -*- coding: utf-8 -*-
"""
Connected components.
"""
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
import networkx as nx
from networkx.utils.decorators import not_implemented_for

__authors__ = "\n".join(['Eben Kenah',
'Aric Hagberg <aric.hagberg@gmail.com>'
'Christopher Ellison'])
__all__ = [
'number_connected_components',
'connected_components',
'connected_component_subgraphs',
'is_connected',
'node_connected_component',
]

@not_implemented_for('directed')
[docs]def connected_components(G):
"""Generate connected components.

Parameters
----------
G : NetworkX graph
An undirected graph

Returns
-------
comp : generator of sets
A generator of sets of nodes, one for each component of G.

Examples
--------
Generate a sorted list of connected components, largest first.

>>> G = nx.path_graph(4)
>>> [len(c) for c in sorted(nx.connected_components(G), key=len, reverse=True)]
[4, 3]

If you only want the largest connected component, it's more
efficient to use max instead of sort.

>>> largest_cc = max(nx.connected_components(G), key=len)

--------
strongly_connected_components

Notes
-----
For undirected graphs only.

"""
seen = set()
for v in G:
if v not in seen:
c = set(_plain_bfs(G, v))
yield c
seen.update(c)

@not_implemented_for('directed')
[docs]def connected_component_subgraphs(G, copy=True):
"""Generate connected components as subgraphs.

Parameters
----------
G : NetworkX graph
An undirected graph.

copy: bool (default=True)
If True make a copy of the graph attributes

Returns
-------
comp : generator
A generator of graphs, one for each connected component of G.

Examples
--------
>>> G = nx.path_graph(4)
>>> graphs = list(nx.connected_component_subgraphs(G))

If you only want the largest connected component, it's more
efficient to use max than sort.

>>> Gc = max(nx.connected_component_subgraphs(G), key=len)

--------
connected_components

Notes
-----
For undirected graphs only.
Graph, node, and edge attributes are copied to the subgraphs by default.

"""
for c in connected_components(G):
if copy:
yield G.subgraph(c).copy()
else:
yield G.subgraph(c)

[docs]def number_connected_components(G):
"""Return the number of connected components.

Parameters
----------
G : NetworkX graph
An undirected graph.

Returns
-------
n : integer
Number of connected components

--------
connected_components

Notes
-----
For undirected graphs only.

"""
return len(list(connected_components(G)))

@not_implemented_for('directed')
[docs]def is_connected(G):
"""Return True if the graph is connected, false otherwise.

Parameters
----------
G : NetworkX Graph
An undirected graph.

Returns
-------
connected : bool
True if the graph is connected, false otherwise.

Examples
--------
>>> G = nx.path_graph(4)
>>> print(nx.is_connected(G))
True

--------
connected_components

Notes
-----
For undirected graphs only.

"""
if len(G) == 0:
raise nx.NetworkXPointlessConcept('Connectivity is undefined ',
'for the null graph.')
return len(set(_plain_bfs(G, next(G.nodes_iter())))) == len(G)

@not_implemented_for('directed')
[docs]def node_connected_component(G, n):
"""Return the nodes in the component of graph containing node n.

Parameters
----------
G : NetworkX Graph
An undirected graph.

n : node label
A node in G

Returns
-------
comp : set
A set of nodes in the component of G containing node n.

--------
connected_components

Notes
-----
For undirected graphs only.

"""
return set(_plain_bfs(G, n))

def _plain_bfs(G, source):
"""A fast BFS node generator"""
seen = set()
nextlevel = {source}
while nextlevel:
thislevel = nextlevel
nextlevel = set()
for v in thislevel:
if v not in seen:
yield v