single_source_dijkstra

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 – 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.

Return type:

dictionaries

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]

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).