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.strongly_connected

# -*- coding: utf-8 -*-
"""Strongly 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 (hagberg@lanl.gov)'
'Christopher Ellison',
'Ben Edwards (bedwards@cs.unm.edu)'])

__all__ = ['number_strongly_connected_components',
'strongly_connected_components',
'strongly_connected_component_subgraphs',
'is_strongly_connected',
'strongly_connected_components_recursive',
'kosaraju_strongly_connected_components',
'condensation']

[docs]@not_implemented_for('undirected')
def strongly_connected_components(G):
"""Generate nodes in strongly connected components of graph.

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

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

Raises
------
NetworkXNotImplemented:
If G is undirected.

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

>>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
>>> [len(c) for c in sorted(nx.strongly_connected_components(G),
...                         key=len, reverse=True)]
[4, 3]

If you only want the largest component, it's more efficient to

>>> largest = max(nx.strongly_connected_components(G), key=len)

--------
connected_components,
weakly_connected_components

Notes
-----
Uses Tarjan's algorithm with Nuutila's modifications.
Nonrecursive version of algorithm.

References
----------
.. [1] Depth-first search and linear graph algorithms, R. Tarjan
SIAM Journal of Computing 1(2):146-160, (1972).

.. [2] On finding the strongly connected components in a directed graph.
E. Nuutila and E. Soisalon-Soinen
Information Processing Letters 49(1): 9-14, (1994)..

"""
preorder = {}
scc_found = {}
scc_queue = []
i = 0     # Preorder counter
for source in G:
if source not in scc_found:
queue = [source]
while queue:
v = queue[-1]
if v not in preorder:
i = i + 1
preorder[v] = i
done = 1
v_nbrs = G[v]
for w in v_nbrs:
if w not in preorder:
queue.append(w)
done = 0
break
if done == 1:
for w in v_nbrs:
if w not in scc_found:
if preorder[w] > preorder[v]:
else:
queue.pop()
scc_found[v] = True
scc = {v}
while scc_queue and preorder[scc_queue[-1]] > preorder[v]:
k = scc_queue.pop()
scc_found[k] = True
yield scc
else:
scc_queue.append(v)

[docs]@not_implemented_for('undirected')
def kosaraju_strongly_connected_components(G, source=None):
"""Generate nodes in strongly connected components of graph.

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

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

Raises
------
NetworkXNotImplemented:
If G is undirected.

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

>>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
>>> [len(c) for c in sorted(nx.kosaraju_strongly_connected_components(G),
...                         key=len, reverse=True)]
[4, 3]

If you only want the largest component, it's more efficient to

>>> largest = max(nx.kosaraju_strongly_connected_components(G), key=len)

--------
connected_components
weakly_connected_components

Notes
-----
Uses Kosaraju's algorithm.

"""
with nx.utils.reversed(G):
post = list(nx.dfs_postorder_nodes(G, source=source))

seen = set()
while post:
r = post.pop()
if r in seen:
continue
c = nx.dfs_preorder_nodes(G, r)
new = {v for v in c if v not in seen}
yield new
seen.update(new)

[docs]@not_implemented_for('undirected')
def strongly_connected_components_recursive(G):
"""Generate nodes in strongly connected components of graph.

Recursive version of algorithm.

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

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

Raises
------
NetworkXNotImplemented:
If G is undirected

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

>>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
>>> [len(c) for c in sorted(nx.strongly_connected_components_recursive(G),
...                         key=len, reverse=True)]
[4, 3]

If you only want the largest component, it's more efficient to

>>> largest = max(nx.strongly_connected_components_recursive(G), key=len)

--------
connected_components

Notes
-----
Uses Tarjan's algorithm with Nuutila's modifications.

References
----------
.. [1] Depth-first search and linear graph algorithms, R. Tarjan
SIAM Journal of Computing 1(2):146-160, (1972).

.. [2] On finding the strongly connected components in a directed graph.
E. Nuutila and E. Soisalon-Soinen
Information Processing Letters 49(1): 9-14, (1994)..

"""
def visit(v, cnt):
root[v] = cnt
visited[v] = cnt
cnt += 1
stack.append(v)
for w in G[v]:
if w not in visited:
for c in visit(w, cnt):
yield c
if w not in component:
root[v] = min(root[v], root[w])
if root[v] == visited[v]:
component[v] = root[v]
tmpc = {v}  # hold nodes in this component
while stack[-1] != v:
w = stack.pop()
component[w] = root[v]
stack.remove(v)
yield tmpc

visited = {}
component = {}
root = {}
cnt = 0
stack = []
for source in G:
if source not in visited:
for c in visit(source, cnt):
yield c

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

Parameters
----------
G : NetworkX Graph
A directed graph.

copy : boolean, optional
if copy is True, Graph, node, and edge attributes are copied to
the subgraphs.

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

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

>>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
>>> [len(Gc) for Gc in sorted(nx.strongly_connected_component_subgraphs(G),
...                         key=len, reverse=True)]
[4, 3]

If you only want the largest component, it's more efficient to

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

--------
connected_component_subgraphs
weakly_connected_component_subgraphs

"""
for comp in strongly_connected_components(G):
if copy:
yield G.subgraph(comp).copy()
else:
yield G.subgraph(comp)

[docs]@not_implemented_for('undirected')
def number_strongly_connected_components(G):
"""Return number of strongly connected components in graph.

Parameters
----------
G : NetworkX graph
A directed graph.

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

--------
connected_components

Notes
-----
For directed graphs only.
"""
return len(list(strongly_connected_components(G)))

[docs]@not_implemented_for('undirected')
def is_strongly_connected(G):
"""Test directed graph for strong connectivity.

Parameters
----------
G : NetworkX Graph
A directed graph.

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

--------
strongly_connected_components

Notes
-----
For directed graphs only.
"""
if len(G) == 0:
raise nx.NetworkXPointlessConcept(
"""Connectivity is undefined for the null graph.""")

return len(list(strongly_connected_components(G))[0]) == len(G)

[docs]@not_implemented_for('undirected')
def condensation(G, scc=None):
"""Returns the condensation of G.

The condensation of G is the graph with each of the strongly connected
components contracted into a single node.

Parameters
----------
G : NetworkX DiGraph
A directed graph.

scc:  list or generator (optional, default=None)
Strongly connected components. If provided, the elements in
scc must partition the nodes in G. If not provided, it will be
calculated as scc=nx.strongly_connected_components(G).

Returns
-------
C : NetworkX DiGraph
The condensation graph C of G. The node labels are integers
corresponding to the index of the component in the list of
strongly connected components of G. C has a graph attribute named
'mapping' with a dictionary mapping the original nodes to the
nodes in C to which they belong. Each node in C also has a node
attribute 'members' with the set of original nodes in G that
form the SCC that the node in C represents.

Raises
------
NetworkXNotImplemented:
If G is not directed

Notes
-----
After contracting all strongly connected components to a single node,
the resulting graph is a directed acyclic graph.

"""
if scc is None:
scc = nx.strongly_connected_components(G)
mapping = {}
members = {}
C = nx.DiGraph()
for i, component in enumerate(scc):
members[i] = component
mapping.update((n, i) for n in component)
number_of_components = i + 1