# all_pairs_dijkstra#

all_pairs_dijkstra(G, cutoff=None, weight='weight')[source]#

Find shortest weighted paths and lengths between all nodes.

Parameters:
GNetworkX graph
cutoffinteger or float, optional

Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff.

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.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 or None to indicate a hidden edge.

Yields:
(node, (distance, path))(node obj, (dict, dict))

Each source node has two associated dicts. The first holds distance keyed by target and the second holds paths keyed by target. (See single_source_dijkstra for the source/target node terminology.) If desired you can apply `dict()` to this function to create a dict keyed by source node to the two dicts.

Notes

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

The yielded dicts only have keys for reachable nodes.

Examples

```>>> G = nx.path_graph(5)
>>> len_path = dict(nx.all_pairs_dijkstra(G))
>>> len_path
2
>>> for node in [0, 1, 2, 3, 4]:
...     print(f"3 - {node}: {len_path[node]}")
3 - 0: 3
3 - 1: 2
3 - 2: 1
3 - 3: 0
3 - 4: 1
>>> len_path
[3, 2, 1]
>>> for n, (dist, path) in nx.all_pairs_dijkstra(G):
...     print(path)
[0, 1]

[2, 1]
[3, 2, 1]
[4, 3, 2, 1]
```