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Source code for networkx.algorithms.shortest_paths.unweighted
# -*- coding: utf-8 -*-
"""
Shortest path algorithms for unweighted graphs.
"""
__author__ = """Aric Hagberg (hagberg@lanl.gov)"""
# Copyright (C) 2004-2010 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
__all__ = ['bidirectional_shortest_path',
'single_source_shortest_path',
'single_source_shortest_path_length',
'all_pairs_shortest_path',
'all_pairs_shortest_path_length',
'predecessor']
import networkx as nx
[docs]def single_source_shortest_path_length(G,source,cutoff=None):
"""Compute the shortest path lengths from source to all reachable nodes.
Parameters
----------
G : NetworkX graph
source : node
Starting node for path
cutoff : integer, optional
Depth to stop the search. Only paths of length <= cutoff are returned.
Returns
-------
lengths : dictionary
Dictionary of shortest path lengths keyed by target.
Examples
--------
>>> G=nx.path_graph(5)
>>> length=nx.single_source_shortest_path_length(G,0)
>>> length[4]
4
>>> print(length)
{0: 0, 1: 1, 2: 2, 3: 3, 4: 4}
See Also
--------
shortest_path_length
"""
seen={} # level (number of hops) when seen in BFS
level=0 # the current level
nextlevel={source:1} # dict of nodes to check at next level
while nextlevel:
thislevel=nextlevel # advance to next level
nextlevel={} # and start a new list (fringe)
for v in thislevel:
if v not in seen:
seen[v]=level # set the level of vertex v
nextlevel.update(G[v]) # add neighbors of v
if (cutoff is not None and cutoff <= level): break
level=level+1
return seen # return all path lengths as dictionary
[docs]def all_pairs_shortest_path_length(G,cutoff=None):
""" Compute the shortest path lengths between all nodes in G.
Parameters
----------
G : NetworkX graph
cutoff : integer, optional
depth to stop the search. Only paths of length <= cutoff are returned.
Returns
-------
lengths : dictionary
Dictionary of shortest path lengths keyed by source and target.
Notes
-----
The dictionary returned only has keys for reachable node pairs.
Examples
--------
>>> G=nx.path_graph(5)
>>> length=nx.all_pairs_shortest_path_length(G)
>>> print(length[1][4])
3
>>> length[1]
{0: 1, 1: 0, 2: 1, 3: 2, 4: 3}
"""
paths={}
for n in G:
paths[n]=single_source_shortest_path_length(G,n,cutoff=cutoff)
return paths
def bidirectional_shortest_path(G,source,target):
"""Return a list of nodes in a shortest path between source and target.
Parameters
----------
G : NetworkX graph
source : node label
starting node for path
target : node label
ending node for path
Returns
-------
path: list
List of nodes in a path from source to target.
Raises
------
NetworkXNoPath
If no path exists between source and target.
See Also
--------
shortest_path
Notes
-----
This algorithm is used by shortest_path(G,source,target).
"""
# call helper to do the real work
results=_bidirectional_pred_succ(G,source,target)
pred,succ,w=results
# build path from pred+w+succ
path=[]
# from source to w
while w is not None:
path.append(w)
w=pred[w]
path.reverse()
# from w to target
w=succ[path[-1]]
while w is not None:
path.append(w)
w=succ[w]
return path
def _bidirectional_pred_succ(G, source, target):
"""Bidirectional shortest path helper.
Returns (pred,succ,w) where
pred is a dictionary of predecessors from w to the source, and
succ is a dictionary of successors from w to the target.
"""
# does BFS from both source and target and meets in the middle
if target == source:
return ({target:None},{source:None},source)
# handle either directed or undirected
if G.is_directed():
Gpred=G.predecessors_iter
Gsucc=G.successors_iter
else:
Gpred=G.neighbors_iter
Gsucc=G.neighbors_iter
# predecesssor and successors in search
pred={source:None}
succ={target:None}
# initialize fringes, start with forward
forward_fringe=[source]
reverse_fringe=[target]
while forward_fringe and reverse_fringe:
if len(forward_fringe) <= len(reverse_fringe):
this_level=forward_fringe
forward_fringe=[]
for v in this_level:
for w in Gsucc(v):
if w not in pred:
forward_fringe.append(w)
pred[w]=v
if w in succ: return pred,succ,w # found path
else:
this_level=reverse_fringe
reverse_fringe=[]
for v in this_level:
for w in Gpred(v):
if w not in succ:
succ[w]=v
reverse_fringe.append(w)
if w in pred: return pred,succ,w # found path
raise nx.NetworkXNoPath("No path between %s and %s." % (source, target))
[docs]def single_source_shortest_path(G,source,cutoff=None):
"""Compute shortest path between source
and all other nodes reachable from source.
Parameters
----------
G : NetworkX graph
source : node label
Starting node for path
cutoff : integer, optional
Depth to stop the search. Only paths of length <= cutoff are returned.
Returns
-------
lengths : dictionary
Dictionary, keyed by target, of shortest paths.
Examples
--------
>>> G=nx.path_graph(5)
>>> path=nx.single_source_shortest_path(G,0)
>>> path[4]
[0, 1, 2, 3, 4]
Notes
-----
The shortest path is not necessarily unique. So there can be multiple
paths between the source and each target node, all of which have the
same 'shortest' length. For each target node, this function returns
only one of those paths.
See Also
--------
shortest_path
"""
level=0 # the current level
nextlevel={source:1} # list of nodes to check at next level
paths={source:[source]} # paths dictionary (paths to key from source)
if cutoff==0:
return paths
while nextlevel:
thislevel=nextlevel
nextlevel={}
for v in thislevel:
for w in G[v]:
if w not in paths:
paths[w]=paths[v]+[w]
nextlevel[w]=1
level=level+1
if (cutoff is not None and cutoff <= level): break
return paths
[docs]def all_pairs_shortest_path(G,cutoff=None):
""" Compute shortest paths between all nodes.
Parameters
----------
G : NetworkX graph
cutoff : integer, optional
Depth to stop the search. Only paths of length <= cutoff are returned.
Returns
-------
lengths : dictionary
Dictionary, keyed by source and target, of shortest paths.
Examples
--------
>>> G=nx.path_graph(5)
>>> path=nx.all_pairs_shortest_path(G)
>>> print(path[0][4])
[0, 1, 2, 3, 4]
See Also
--------
floyd_warshall()
"""
paths={}
for n in G:
paths[n]=single_source_shortest_path(G,n,cutoff=cutoff)
return paths
[docs]def predecessor(G,source,target=None,cutoff=None,return_seen=None):
""" Returns dictionary of predecessors for the path from source to all nodes in G.
Parameters
----------
G : NetworkX graph
source : node label
Starting node for path
target : node label, optional
Ending node for path. If provided only predecessors between
source and target are returned
cutoff : integer, optional
Depth to stop the search. Only paths of length <= cutoff are returned.
Returns
-------
pred : dictionary
Dictionary, keyed by node, of predecessors in the shortest path.
Examples
--------
>>> G=nx.path_graph(4)
>>> print(G.nodes())
[0, 1, 2, 3]
>>> nx.predecessor(G,0)
{0: [], 1: [0], 2: [1], 3: [2]}
"""
level=0 # the current level
nextlevel=[source] # list of nodes to check at next level
seen={source:level} # level (number of hops) when seen in BFS
pred={source:[]} # predecessor dictionary
while nextlevel:
level=level+1
thislevel=nextlevel
nextlevel=[]
for v in thislevel:
for w in G[v]:
if w not in seen:
pred[w]=[v]
seen[w]=level
nextlevel.append(w)
elif (seen[w]==level):# add v to predecessor list if it
pred[w].append(v) # is at the correct level
if (cutoff and cutoff <= level):
break
if target is not None:
if return_seen:
if not target in pred: return ([],-1) # No predecessor
return (pred[target],seen[target])
else:
if not target in pred: return [] # No predecessor
return pred[target]
else:
if return_seen:
return (pred,seen)
else:
return pred