"""Weakly connected components."""
import networkx as nx
from networkx.utils.decorators import not_implemented_for
__all__ = [
"number_weakly_connected_components",
"weakly_connected_components",
"is_weakly_connected",
]
[docs]@not_implemented_for("undirected")
def weakly_connected_components(G):
"""Generate weakly connected components of G.
Parameters
----------
G : NetworkX graph
A directed graph
Returns
-------
comp : generator of sets
A generator of sets of nodes, one for each weakly connected
component of G.
Raises
------
NetworkXNotImplemented
If G is undirected.
Examples
--------
Generate a sorted list of weakly connected components, largest first.
>>> G = nx.path_graph(4, create_using=nx.DiGraph())
>>> nx.add_path(G, [10, 11, 12])
>>> [
... len(c)
... for c in sorted(nx.weakly_connected_components(G), key=len, reverse=True)
... ]
[4, 3]
If you only want the largest component, it's more efficient to
use max instead of sort:
>>> largest_cc = max(nx.weakly_connected_components(G), key=len)
See Also
--------
connected_components
strongly_connected_components
Notes
-----
For directed graphs only.
"""
seen = set()
for v in G:
if v not in seen:
c = set(_plain_bfs(G, v))
yield c
seen.update(c)
[docs]@not_implemented_for("undirected")
def number_weakly_connected_components(G):
"""Returns the number of weakly connected components in G.
Parameters
----------
G : NetworkX graph
A directed graph.
Returns
-------
n : integer
Number of weakly connected components
Raises
------
NetworkXNotImplemented
If G is undirected.
See Also
--------
weakly_connected_components
number_connected_components
number_strongly_connected_components
Notes
-----
For directed graphs only.
"""
return sum(1 for wcc in weakly_connected_components(G))
[docs]@not_implemented_for("undirected")
def is_weakly_connected(G):
"""Test directed graph for weak connectivity.
A directed graph is weakly connected if and only if the graph
is connected when the direction of the edge between nodes is ignored.
Note that if a graph is strongly connected (i.e. the graph is connected
even when we account for directionality), it is by definition weakly
connected as well.
Parameters
----------
G : NetworkX Graph
A directed graph.
Returns
-------
connected : bool
True if the graph is weakly connected, False otherwise.
Raises
------
NetworkXNotImplemented
If G is undirected.
See Also
--------
is_strongly_connected
is_semiconnected
is_connected
is_biconnected
weakly_connected_components
Notes
-----
For directed graphs only.
"""
if len(G) == 0:
raise nx.NetworkXPointlessConcept(
"""Connectivity is undefined for the null graph."""
)
return len(list(weakly_connected_components(G))[0]) == len(G)
def _plain_bfs(G, source):
"""A fast BFS node generator
The direction of the edge between nodes is ignored.
For directed graphs only.
"""
Gsucc = G.succ
Gpred = G.pred
seen = set()
nextlevel = {source}
while nextlevel:
thislevel = nextlevel
nextlevel = set()
for v in thislevel:
if v not in seen:
yield v
seen.add(v)
nextlevel.update(Gsucc[v])
nextlevel.update(Gpred[v])