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

Compute shortest path lengths between all nodes in a weighted graph.

  • G (NetworkX graph)

  • 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.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.


distance – (source, dictionary) iterator with dictionary keyed by target and shortest path length as the key value.

Return type:



>>> G = nx.path_graph(5)
>>> length = dict(nx.all_pairs_dijkstra_path_length(G))
>>> for node in [0, 1, 2, 3, 4]:
...     print('1 - {}: {}'.format(node, length[1][node]))
1 - 0: 1
1 - 1: 0
1 - 2: 1
1 - 3: 2
1 - 4: 3
>>> length[3][2]
>>> length[2][2]


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

The dictionary returned only has keys for reachable node pairs.