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.shortest_paths.generic

# -*- coding: utf-8 -*-
"""
Compute the shortest paths and path lengths between nodes in the graph.

These algorithms work with undirected and directed graphs.

"""
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
import networkx as nx
__author__ = """\n""".join(['Aric Hagberg <aric.hagberg@gmail.com>',
'Sérgio Nery Simões <sergionery@gmail.com>'])
__all__ = ['shortest_path', 'all_shortest_paths',
'shortest_path_length', 'average_shortest_path_length',
'has_path']

[docs]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

[docs]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 using all nodes as source nodes.

target : node, optional
Ending node for path.
If not specified, compute shortest paths using all nodes as target nodes.

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
All returned paths include both the source and target in the path.

If the source and target are both specified, return a single list
of nodes in a shortest path from the source to the target.

If only the source is specified, return a dictionary keyed by
targets with a list of nodes in a shortest path from the source
to one of the targets.

If only the target is specified, return a dictionary keyed by
sources with a list of nodes in a shortest path from one of the
sources to the target.

If neither the source nor target are 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,target=4) # source not specified
>>> p[0]
[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.

--------
all_pairs_shortest_path()
all_pairs_dijkstra_path()
single_source_shortest_path()
single_source_dijkstra_path()
"""
if source is None:
if target is None:
## Find paths between all pairs.
if weight is None:
paths=nx.all_pairs_shortest_path(G)
else:
paths=nx.all_pairs_dijkstra_path(G,weight=weight)
else:
## Find paths from all nodes co-accessible to the target.
with nx.utils.reversed(G):
if weight is None:
paths=nx.single_source_shortest_path(G, target)
else:
paths=nx.single_source_dijkstra_path(G, target, weight=weight)

# Now flip the paths so they go from a source to the target.
for target in paths:
paths[target] = list(reversed(paths[target]))

else:
if target is None:
## Find paths to all nodes accessible from the source.
if weight is None:
paths=nx.single_source_shortest_path(G,source)
else:
paths=nx.single_source_dijkstra_path(G,source,weight=weight)
else:
## Find 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

[docs]def shortest_path_length(G, source=None, target=None, weight=None):
"""Compute shortest path lengths in the graph.

Parameters
----------
G : NetworkX graph

source : node, optional
Starting node for path.
If not specified, compute shortest path lengths using all nodes as
source nodes.

target : node, optional
Ending node for path.
If not specified, compute shortest path lengths using all nodes as
target nodes.

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: int or dictionary
If the source and target are both specified, return the length of
the shortest path from the source to the target.

If only the source is specified, return a dictionary keyed by
targets whose values are the lengths of the shortest path from the
source to one of the targets.

If only the target is specified, return a dictionary keyed by
sources whose values are the lengths of the shortest path from one
of the sources to the target.

If neither the source nor target are specified return a dictionary
of dictionaries with path[source][target]=L, where L is the length
of the shortest path from source to target.

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,target=4) # source not specified
>>> p[0]
4
>>> p=nx.shortest_path_length(G) # source,target not specified
>>> p[0][4]
4

Notes
-----
The length of the path is always 1 less than the number of nodes involved
in the path since the length measures the number of edges followed.

For digraphs this returns the shortest directed path length. To find path
lengths in the reverse direction use G.reverse(copy=False) first to flip
the edge orientation.

--------
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:
## Find paths between all pairs.
if weight is None:
paths=nx.all_pairs_shortest_path_length(G)
else:
paths=nx.all_pairs_dijkstra_path_length(G, weight=weight)
else:
## Find paths from all nodes co-accessible to the target.
with nx.utils.reversed(G):
if weight is None:
paths=nx.single_source_shortest_path_length(G, target)
else:
paths=nx.single_source_dijkstra_path_length(G, target,
weight=weight)
else:
if target is None:
## Find paths to all nodes accessible from the source.
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:
## Find 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

[docs]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))

[docs]def all_shortest_paths(G, source, target, weight=None):
"""Compute all shortest paths in the graph.

Parameters
----------
G : NetworkX graph

source : node
Starting node for path.

target : node
Ending node for path.

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
-------
paths: generator of lists
A generator of all paths between source and target.

Examples
--------
>>> G=nx.Graph()
>>> print([p for p in nx.all_shortest_paths(G,source=0,target=2)])
[[0, 1, 2], [0, 10, 2]]

Notes
-----
There may be many shortest paths between the source and target.

--------
shortest_path()
single_source_shortest_path()
all_pairs_shortest_path()
"""
if weight is not None:
pred,dist = nx.dijkstra_predecessor_and_distance(G,source,weight=weight)
else:
pred = nx.predecessor(G,source)
if target not in pred:
raise nx.NetworkXNoPath()
stack = [[target,0]]
top = 0
while top >= 0:
node,i = stack[top]
if node == source:
yield [p for p,n in reversed(stack[:top+1])]
if len(pred[node]) > i:
top += 1
if top == len(stack):
stack.append([pred[node][i],0])
else:
stack[top] = [pred[node][i],0]
else:
stack[top-1][1] += 1
top -= 1