9.7.6.9. networkx.algorithms.shortest_paths.weighted.single_source_dijkstra

networkx.algorithms.shortest_paths.weighted.single_source_dijkstra(G, source, target=None, cutoff=None, weight='weight')[source]

Find shortest weighted paths and lengths from a source node.

Compute the shortest path length between source and all other reachable nodes for a weighted graph.

Uses Dijkstra’s algorithm to compute shortest paths and lengths between a source and all other reachable nodes in a weighted graph.

Parameters:

G : NetworkX graph

source : node label

Starting node for path

target : node label, optional

Ending node for path

cutoff : integer or float, optional

Depth to stop the search. Only return paths with length <= cutoff.

weight : string or function

If this is a string, then edge weights will be accessed via the edge attribute with this key (that is, the weight of the edge joining u to v will be G.edge[u][v][weight]). If no such edge attribute exists, the weight of the edge is assumed to be one.

If this is a function, the weight of an edge is the value returned by the function. The function must accept exactly three positional arguments: the two endpoints of an edge and the dictionary of edge attributes for that edge. The function must return a number.
Returns:

distance,path : dictionaries

Returns a tuple of two dictionaries keyed by node. The first dictionary stores distance from the source. The second stores the path from the source to that node.

See also

single_source_dijkstra_path, single_source_dijkstra_path_length, single_source_bellman_ford

Notes

Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.

The weight function can be used to hide edges by returning None. So weight = lambda u, v, d: 1 if d['color']=="red" else None will find the shortest red path.

Based on the Python cookbook recipe (119466) at http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/119466

This algorithm is not guaranteed to work if edge weights are negative or are floating point numbers (overflows and roundoff errors can cause problems).

Examples

>>> G=nx.path_graph(5)
>>> length,path=nx.single_source_dijkstra(G,0)
>>> print(length[4])
4
>>> print(length)
{0: 0, 1: 1, 2: 2, 3: 3, 4: 4}
>>> path[4]
[0, 1, 2, 3, 4]