dijkstra_path#

dijkstra_path(G, source, target, weight='weight')[source]#

Returns the shortest weighted path from source to target in G.

Uses Dijkstra’s Method to compute the shortest weighted path between two nodes in a graph.

Parameters:

GNetworkX graph

sourcenode

Starting node

targetnode

Ending node

weightstring 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.edges[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 or None to indicate a hidden edge.

Returns:

pathlist: List of nodes in a shortest path.

Raises:

NodeNotFound: If source is not in G.
NetworkXNoPath: If no path exists between source and target.

See also

bidirectional_dijkstra
bellman_ford_path
single_source_dijkstra

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.

The weight function can be used to include node weights.

>>> def func(u, v, d):
...     node_u_wt = G.nodes[u].get("node_weight", 1)
...     node_v_wt = G.nodes[v].get("node_weight", 1)
...     edge_wt = d.get("weight", 1)
...     return node_u_wt / 2 + node_v_wt / 2 + edge_wt

In this example we take the average of start and end node weights of an edge and add it to the weight of the edge.

The function single_source_dijkstra() computes both path and length-of-path if you need both, use that.

Examples

>>> G = nx.path_graph(5)
>>> print(nx.dijkstra_path(G, 0, 4))
[0, 1, 2, 3, 4]

Find edges of shortest path in Multigraph

>>> G = nx.MultiDiGraph()
>>> G.add_weighted_edges_from([(1, 2, 0.75), (1, 2, 0.5), (2, 3, 0.5), (1, 3, 1.5)])
>>> nodes = nx.dijkstra_path(G, 1, 3)
>>> edges = nx.utils.pairwise(nodes)
>>> list((u, v, min(G[u][v], key=lambda k: G[u][v][k].get('weight', 1))) for u, v in edges)
[(1, 2, 1), (2, 3, 0)]