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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.
"""
# Copyright (C) 2004-2013 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
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']
@not_implemented_for('undirected')
[docs]def strongly_connected_components(G):
"""Generate nodes in strongly connected components of graph.
Parameters
----------
G : NetworkX Graph
An directed graph.
Returns
-------
comp : generator of lists
A list of nodes for each strongly connected component of G.
Raises
------
NetworkXNotImplemented: If G is undirected.
See Also
--------
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={}
lowlink={}
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:
lowlink[v]=preorder[v]
for w in v_nbrs:
if w not in scc_found:
if preorder[w]>preorder[v]:
lowlink[v]=min([lowlink[v],lowlink[w]])
else:
lowlink[v]=min([lowlink[v],preorder[w]])
queue.pop()
if lowlink[v]==preorder[v]:
scc_found[v]=True
scc=[v]
while scc_queue and preorder[scc_queue[-1]]>preorder[v]:
k=scc_queue.pop()
scc_found[k]=True
scc.append(k)
yield scc
else:
scc_queue.append(v)
@not_implemented_for('undirected')
[docs]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 lists
A list of nodes for each component of G.
Raises
------
NetworkXNotImplemented: If G is undirected.
See Also
--------
connected_components
Notes
-----
Uses Kosaraju's algorithm.
"""
with nx.utils.reversed(G):
post = list(nx.dfs_postorder_nodes(G, source=source))
seen = {}
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]
seen.update([(u,True) for u in new])
yield new
@not_implemented_for('undirected')
[docs]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 lists
A list of nodes for each component of G.
The list is ordered from largest connected component to smallest.
Raises
------
NetworkXNotImplemented : If G is undirected
See Also
--------
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]
tmpc.append(w)
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
@not_implemented_for('undirected')
[docs]def strongly_connected_component_subgraphs(G, copy=True):
"""Generate strongly connected components as subgraphs.
Parameters
----------
G : NetworkX Graph
A graph.
Returns
-------
comp : generator of lists
A list of graphs, one for each strongly connected component of G.
copy : boolean
if copy is True, Graph, node, and edge attributes are copied to
the subgraphs.
See Also
--------
connected_component_subgraphs
"""
for comp in strongly_connected_components(G):
if copy:
yield G.subgraph(comp).copy()
else:
yield G.subgraph(comp)
@not_implemented_for('undirected')
[docs]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
See Also
--------
connected_components
Notes
-----
For directed graphs only.
"""
return len(list(strongly_connected_components(G)))
@not_implemented_for('undirected')
[docs]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.
See Also
--------
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)
@not_implemented_for('undirected')
[docs]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 list 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
C.add_nodes_from(range(number_of_components))
C.add_edges_from((mapping[u], mapping[v]) for u, v in G.edges_iter()
if mapping[u] != mapping[v])
# Add a list of members (ie original nodes) to each node (ie scc) in C.
nx.set_node_attributes(C, 'members', members)
# Add mapping dict as graph attribute
C.graph['mapping'] = mapping
return C
```