all_pairs_dijkstra

all_pairs_dijkstra(G, cutoff=None, weight='weight')

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

Additional backends implement this function

cugraphGPU-accelerated backend.

Additional parameters:

dtypedtype or None, optional

The data type (np.float32, np.float64, or None) to use for the edge weights in the algorithm. If None, then dtype is determined by the edge values.

parallelA networkx backend that uses joblib to run graph algorithms in parallel. Find the nx-parallel’s configuration guide here

The parallel implementation first divides the nodes into chunks and then creates a generator to lazily compute shortest paths and lengths for each node_chunk, and then employs joblib’s Parallel function to execute these computations in parallel across n_jobs number of CPU cores.

Additional parameters:

get_chunksstr, function (default = “chunks”)

A function that takes in an iterable of all the nodes as input and returns an iterable node_chunks. The default chunking is done by slicing the G.nodes into n_jobs number of chunks.

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