/usr/share/pyshared/networkx/algorithms/shortest_paths/generic.py is in python-networkx 1.6-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 | # -*- coding: utf-8 -*-
"""
Compute the shortest paths and path lengths between nodes in the graph.
These algorithms work with undirected and directed graphs.
For directed graphs the paths can be computed in the reverse
order by first flipping the edge orientation using R=G.reverse(copy=False).
"""
__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__ = ['shortest_path',
'shortest_path_length',
'average_shortest_path_length',
'has_path']
import networkx as nx
def has_path(G, source ,target):
"""Return true if G has a path from source to target.
False otherwise.
Parameters
----------
G : NetworkX graph
source : node
Starting node for path.
target : node
Ending node for path.
"""
try:
sp = nx.shortest_path(G,source, target)
except nx.NetworkXNoPath:
return False
return True
def shortest_path(G, source=None, target=None, weight=None):
"""Compute shortest paths in the graph.
Parameters
----------
G : NetworkX graph
source : node, optional
Starting node for path.
If not specified compute shortest paths for all connected node pairs.
target : node, optional
Ending node for path.
If not specified compute shortest paths for every node reachable
from the source.
weight : None or string, optional (default = None)
If None, every edge has weight/distance/cost 1.
If a string, use this edge attribute as the edge weight.
Any edge attribute not present defaults to 1.
Returns
-------
path: list or dictionary
If the source and target are both specified return a single list
of nodes in a shortest path.
If only the source is specified return a dictionary keyed by
targets with a list of nodes in a shortest path.
If neither the source or target is specified return a dictionary
of dictionaries with path[source][target]=[list of nodes in path].
Examples
--------
>>> G=nx.path_graph(5)
>>> print(nx.shortest_path(G,source=0,target=4))
[0, 1, 2, 3, 4]
>>> p=nx.shortest_path(G,source=0) # target not specified
>>> p[4]
[0, 1, 2, 3, 4]
>>> p=nx.shortest_path(G) # source,target not specified
>>> p[0][4]
[0, 1, 2, 3, 4]
Notes
-----
There may be more than one shortest path between a source and target.
This returns only one of them.
For digraphs this returns a shortest directed path.
To find paths in the reverse direction use G.reverse(copy=False)
first to flip the edge orientation.
See Also
--------
all_pairs_shortest_path()
all_pairs_dijkstra_path()
single_source_shortest_path()
single_source_dijkstra_path()
"""
if source is None:
if target is None:
if weight is None:
paths=nx.all_pairs_shortest_path(G)
else:
paths=nx.all_pairs_dijkstra_path(G,weight=weight)
else:
raise nx.NetworkXError(\
"Target given but no source specified.")
else: # source specified
if target is None:
if weight is None:
paths=nx.single_source_shortest_path(G,source)
else:
paths=nx.single_source_dijkstra_path(G,source,weight=weight)
else:
# shortest source-target path
if weight is None:
paths=nx.bidirectional_shortest_path(G,source,target)
else:
paths=nx.dijkstra_path(G,source,target,weight)
return paths
def shortest_path_length(G, source=None, target=None, weight=None):
"""Compute shortest path lengths in the graph.
This function can compute the single source shortest path
lengths by specifying only the source or all pairs shortest
path lengths by specifying neither the source or target.
Parameters
----------
G : NetworkX graph
source : node, optional
Starting node for path.
If not specified compute shortest path lengths for all
connected node pairs.
target : node, optional
Ending node for path.
If not specified compute shortest path lengths for every
node reachable from the source.
weight : None or string, optional (default = None)
If None, every edge has weight/distance/cost 1.
If a string, use this edge attribute as the edge weight.
Any edge attribute not present defaults to 1.
Returns
-------
length : number, or container of numbers
If the source and target are both specified return a
single number for the shortest path.
If only the source is specified return a dictionary keyed by
targets with a the shortest path as keys.
If neither the source or target is specified return a dictionary
of dictionaries with length[source][target]=value.
Raises
------
NetworkXNoPath
If no path exists between source and target.
Examples
--------
>>> G=nx.path_graph(5)
>>> print(nx.shortest_path_length(G,source=0,target=4))
4
>>> p=nx.shortest_path_length(G,source=0) # target not specified
>>> p[4]
4
>>> p=nx.shortest_path_length(G) # source,target not specified
>>> p[0][4]
4
Notes
-----
For digraphs this returns the shortest directed path.
To find path lengths in the reverse direction use G.reverse(copy=False)
first to flip the edge orientation.
See Also
--------
all_pairs_shortest_path_length()
all_pairs_dijkstra_path_length()
single_source_shortest_path_length()
single_source_dijkstra_path_length()
"""
if source is None:
if target is None:
if weight is None:
paths=nx.all_pairs_shortest_path_length(G)
else:
paths=nx.all_pairs_dijkstra_path_length(G, weight=weight)
else:
raise nx.NetworkXError(\
"Target given but no source specified.")
else: # source specified
if target is None:
if weight is None:
paths=nx.single_source_shortest_path_length(G,source)
else:
paths=nx.single_source_dijkstra_path_length(G,source,weight=weight)
else:
# shortest source-target path
if weight is None:
p=nx.bidirectional_shortest_path(G,source,target)
paths=len(p)-1
else:
paths=nx.dijkstra_path_length(G,source,target,weight)
return paths
def average_shortest_path_length(G, weight=None):
r"""Return the average shortest path length.
The average shortest path length is
.. math::
a =\sum_{s,t \in V} \frac{d(s, t)}{n(n-1)}
where `V` is the set of nodes in `G`,
`d(s, t)` is the shortest path from `s` to `t`,
and `n` is the number of nodes in `G`.
Parameters
----------
G : NetworkX graph
weight : None or string, optional (default = None)
If None, every edge has weight/distance/cost 1.
If a string, use this edge attribute as the edge weight.
Any edge attribute not present defaults to 1.
Raises
------
NetworkXError:
if the graph is not connected.
Examples
--------
>>> G=nx.path_graph(5)
>>> print(nx.average_shortest_path_length(G))
2.0
For disconnected graphs you can compute the average shortest path
length for each component:
>>> G=nx.Graph([(1,2),(3,4)])
>>> for g in nx.connected_component_subgraphs(G):
... print(nx.average_shortest_path_length(g))
1.0
1.0
"""
if G.is_directed():
if not nx.is_weakly_connected(G):
raise nx.NetworkXError("Graph is not connected.")
else:
if not nx.is_connected(G):
raise nx.NetworkXError("Graph is not connected.")
avg=0.0
if weight is None:
for node in G:
path_length=nx.single_source_shortest_path_length(G, node)
avg += sum(path_length.values())
else:
for node in G:
path_length=nx.single_source_dijkstra_path_length(G, node, weight=weight)
avg += sum(path_length.values())
n=len(G)
return avg/(n*(n-1))
|