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.dag
# -*- coding: utf-8 -*-
from fractions import gcd
import networkx as nx
"""Algorithms for directed acyclic graphs (DAGs)."""
# Copyright (C) 2006-2011 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
__author__ = """\n""".join(['Aric Hagberg <aric.hagberg@gmail.com>',
'Dan Schult (dschult@colgate.edu)',
'Ben Edwards (bedwards@cs.unm.edu)'])
__all__ = ['descendants',
'ancestors',
'topological_sort',
'topological_sort_recursive',
'is_directed_acyclic_graph',
'is_aperiodic']
[docs]def descendants(G, source):
"""Return all nodes reachable from `source` in G.
Parameters
----------
G : NetworkX DiGraph
source : node in G
Returns
-------
des : set()
The descendants of source in G
"""
if not G.has_node(source):
raise nx.NetworkXError("The node %s is not in the graph." % source)
des = set(nx.shortest_path_length(G, source=source).keys()) - set([source])
return des
[docs]def ancestors(G, source):
"""Return all nodes having a path to `source` in G.
Parameters
----------
G : NetworkX DiGraph
source : node in G
Returns
-------
ancestors : set()
The ancestors of source in G
"""
if not G.has_node(source):
raise nx.NetworkXError("The node %s is not in the graph." % source)
anc = set(nx.shortest_path_length(G, target=source).keys()) - set([source])
return anc
[docs]def is_directed_acyclic_graph(G):
"""Return True if the graph G is a directed acyclic graph (DAG) or
False if not.
Parameters
----------
G : NetworkX graph
A graph
Returns
-------
is_dag : bool
True if G is a DAG, false otherwise
"""
if not G.is_directed():
return False
try:
topological_sort(G, reverse=True)
return True
except nx.NetworkXUnfeasible:
return False
[docs]def topological_sort(G, nbunch=None, reverse=False):
"""Return a list of nodes in topological sort order.
A topological sort is a nonunique permutation of the nodes
such that an edge from u to v implies that u appears before v in the
topological sort order.
Parameters
----------
G : NetworkX digraph
A directed graph
nbunch : container of nodes (optional)
Explore graph in specified order given in nbunch
reverse : bool, optional
Return postorder instead of preorder if True.
Reverse mode is a bit more efficient.
Raises
------
NetworkXError
Topological sort is defined for directed graphs only. If the
graph G is undirected, a NetworkXError is raised.
NetworkXUnfeasible
If G is not a directed acyclic graph (DAG) no topological sort
exists and a NetworkXUnfeasible exception is raised.
Notes
-----
This algorithm is based on a description and proof in
The Algorithm Design Manual [1]_ .
See also
--------
is_directed_acyclic_graph
References
----------
.. [1] Skiena, S. S. The Algorithm Design Manual (Springer-Verlag, 1998).
http://www.amazon.com/exec/obidos/ASIN/0387948600/ref=ase_thealgorithmrepo/
"""
if not G.is_directed():
raise nx.NetworkXError(
"Topological sort not defined on undirected graphs.")
# nonrecursive version
seen = set()
order = []
explored = set()
if nbunch is None:
nbunch = G.nodes_iter()
for v in nbunch: # process all vertices in G
if v in explored:
continue
fringe = [v] # nodes yet to look at
while fringe:
w = fringe[-1] # depth first search
if w in explored: # already looked down this branch
fringe.pop()
continue
seen.add(w) # mark as seen
# Check successors for cycles and for new nodes
new_nodes = []
for n in G[w]:
if n not in explored:
if n in seen: #CYCLE !!
raise nx.NetworkXUnfeasible("Graph contains a cycle.")
new_nodes.append(n)
if new_nodes: # Add new_nodes to fringe
fringe.extend(new_nodes)
else: # No new nodes so w is fully explored
explored.add(w)
order.append(w)
fringe.pop() # done considering this node
if reverse:
return order
else:
return list(reversed(order))
[docs]def topological_sort_recursive(G, nbunch=None, reverse=False):
"""Return a list of nodes in topological sort order.
A topological sort is a nonunique permutation of the nodes such
that an edge from u to v implies that u appears before v in the
topological sort order.
Parameters
----------
G : NetworkX digraph
nbunch : container of nodes (optional)
Explore graph in specified order given in nbunch
reverse : bool, optional
Return postorder instead of preorder if True.
Reverse mode is a bit more efficient.
Raises
------
NetworkXError
Topological sort is defined for directed graphs only. If the
graph G is undirected, a NetworkXError is raised.
NetworkXUnfeasible
If G is not a directed acyclic graph (DAG) no topological sort
exists and a NetworkXUnfeasible exception is raised.
Notes
-----
This is a recursive version of topological sort.
See also
--------
topological_sort
is_directed_acyclic_graph
"""
if not G.is_directed():
raise nx.NetworkXError(
"Topological sort not defined on undirected graphs.")
def _dfs(v):
ancestors.add(v)
for w in G[v]:
if w in ancestors:
raise nx.NetworkXUnfeasible("Graph contains a cycle.")
if w not in explored:
_dfs(w)
ancestors.remove(v)
explored.add(v)
order.append(v)
ancestors = set()
explored = set()
order = []
if nbunch is None:
nbunch = G.nodes_iter()
for v in nbunch:
if v not in explored:
_dfs(v)
if reverse:
return order
else:
return list(reversed(order))
[docs]def is_aperiodic(G):
"""Return True if G is aperiodic.
A directed graph is aperiodic if there is no integer k > 1 that
divides the length of every cycle in the graph.
Parameters
----------
G : NetworkX DiGraph
Graph
Returns
-------
aperiodic : boolean
True if the graph is aperiodic False otherwise
Raises
------
NetworkXError
If G is not directed
Notes
-----
This uses the method outlined in [1]_, which runs in O(m) time
given m edges in G. Note that a graph is not aperiodic if it is
acyclic as every integer trivial divides length 0 cycles.
References
----------
.. [1] Jarvis, J. P.; Shier, D. R. (1996),
Graph-theoretic analysis of finite Markov chains,
in Shier, D. R.; Wallenius, K. T., Applied Mathematical Modeling:
A Multidisciplinary Approach, CRC Press.
"""
if not G.is_directed():
raise nx.NetworkXError("is_aperiodic not defined for undirected graphs")
s = next(G.nodes_iter())
levels = {s:0}
this_level = [s]
g = 0
l = 1
while this_level:
next_level = []
for u in this_level:
for v in G[u]:
if v in levels: # Non-Tree Edge
g = gcd(g, levels[u]-levels[v] + 1)
else: # Tree Edge
next_level.append(v)
levels[v] = l
this_level = next_level
l += 1
if len(levels)==len(G): #All nodes in tree
return g==1
else:
return g==1 and nx.is_aperiodic(G.subgraph(set(G)-set(levels)))