# -*- coding: utf-8 -*-
# Copyright (C) 2004-2018 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
#
# Authors: Eben Kenah
# Aric Hagberg (hagberg@lanl.gov)
# Christopher Ellison
# Ben Edwards (bedwards@cs.unm.edu)
"""Strongly connected components."""
import warnings as _warnings
import networkx as nx
from networkx.utils.decorators import not_implemented_for
__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
A 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())
>>> nx.add_cycle(G, [10, 11, 12])
>>> [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
use max instead of sort.
>>> largest = max(nx.strongly_connected_components(G), key=len)
See Also
--------
connected_components
weakly_connected_components
kosaraju_strongly_connected_components
Notes
-----
Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_.
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)..
"""
nbrs = {}
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
if v not in nbrs:
nbrs[v] = iter(G[v])
v_nbrs = nbrs[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 G[v]:
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.add(k)
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
A 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())
>>> nx.add_cycle(G, [10, 11, 12])
>>> [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
use max instead of sort.
>>> largest = max(nx.kosaraju_strongly_connected_components(G), key=len)
See Also
--------
strongly_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
A 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())
>>> nx.add_cycle(G, [10, 11, 12])
>>> [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
use max instead of sort.
>>> largest = max(nx.strongly_connected_components_recursive(G), key=len)
See Also
--------
connected_components
Notes
-----
Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_.
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.add(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
[docs]@not_implemented_for('undirected')
def strongly_connected_component_subgraphs(G, copy=True):
"""DEPRECATED: Use ``(G.subgraph(c) for c in strongly_connected_components(G))``
Or ``(G.subgraph(c).copy() for c in strongly_connected_components(G))``
"""
msg = "strongly_connected_component_subgraphs is deprecated and will be removed in 2.2" \
"use (G.subgraph(c).copy() for c in strongly_connected_components(G))"
_warnings.warn(msg, DeprecationWarning)
for c in strongly_connected_components(G):
if copy:
yield G.subgraph(c).copy()
else:
yield G.subgraph(c)
[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
Raises
------
NetworkXNotImplemented:
If G is undirected.
See Also
--------
strongly_connected_components
number_connected_components
number_weakly_connected_components
Notes
-----
For directed graphs only.
"""
return sum(1 for scc in strongly_connected_components(G))
[docs]@not_implemented_for('undirected')
def is_strongly_connected(G):
"""Test directed graph for strong connectivity.
A directed graph is strongly connected if and only if every vertex in
the graph is reachable from every other vertex.
Parameters
----------
G : NetworkX Graph
A directed graph.
Returns
-------
connected : bool
True if the graph is strongly connected, False otherwise.
Raises
------
NetworkXNotImplemented:
If G is undirected.
See Also
--------
is_weakly_connected
is_semiconnected
is_connected
is_biconnected
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 undirected.
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()
# Add mapping dict as graph attribute
C.graph['mapping'] = mapping
if len(G) == 0:
return C
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()
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')
return C