# Source code for networkx.algorithms.components.connected

```
"""Connected components."""
import networkx as nx
from networkx.utils.decorators import not_implemented_for
from ...utils import arbitrary_element
__all__ = [
"number_connected_components",
"connected_components",
"is_connected",
"node_connected_component",
]
[docs]@not_implemented_for("directed")
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.
Raises
------
NetworkXNotImplemented
If G is directed.
Examples
--------
Generate a sorted list of connected components, largest first.
>>> G = nx.path_graph(4)
>>> nx.add_path(G, [10, 11, 12])
>>> [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)
To create the induced subgraph of each component use:
>>> S = [G.subgraph(c).copy() for c in nx.connected_components(G)]
See Also
--------
strongly_connected_components
weakly_connected_components
Notes
-----
For undirected graphs only.
"""
seen = set()
for v in G:
if v not in seen:
c = _plain_bfs(G, v)
seen.update(c)
yield c
[docs]def number_connected_components(G):
"""Returns the number of connected components.
Parameters
----------
G : NetworkX graph
An undirected graph.
Returns
-------
n : integer
Number of connected components
See Also
--------
connected_components
number_weakly_connected_components
number_strongly_connected_components
Notes
-----
For undirected graphs only.
"""
return sum(1 for cc in connected_components(G))
[docs]@not_implemented_for("directed")
def is_connected(G):
"""Returns 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.
Raises
------
NetworkXNotImplemented
If G is directed.
Examples
--------
>>> G = nx.path_graph(4)
>>> print(nx.is_connected(G))
True
See Also
--------
is_strongly_connected
is_weakly_connected
is_semiconnected
is_biconnected
connected_components
Notes
-----
For undirected graphs only.
"""
if len(G) == 0:
raise nx.NetworkXPointlessConcept(
"Connectivity is undefined ", "for the null graph."
)
return sum(1 for node in _plain_bfs(G, arbitrary_element(G))) == len(G)
[docs]@not_implemented_for("directed")
def node_connected_component(G, n):
"""Returns the set of 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.
Raises
------
NetworkXNotImplemented
If G is directed.
See Also
--------
connected_components
Notes
-----
For undirected graphs only.
"""
return _plain_bfs(G, n)
def _plain_bfs(G, source):
"""A fast BFS node generator"""
G_adj = G.adj
seen = set()
nextlevel = {source}
while nextlevel:
thislevel = nextlevel
nextlevel = set()
for v in thislevel:
if v not in seen:
seen.add(v)
nextlevel.update(G_adj[v])
return seen
```