# single_source_bellman_ford#

single_source_bellman_ford(G, source, target=None, weight='weight')[source]#

Compute shortest paths and lengths in a weighted graph G.

Uses Bellman-Ford algorithm for shortest paths.

Parameters:
GNetworkX graph
sourcenode label

Starting node for path

targetnode label, optional

Ending node for path

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.

Returns:
distance, pathpair of dictionaries, or numeric and list

If target is None, returns a tuple of two dictionaries keyed by node. The first dictionary stores distance from one of the source nodes. The second stores the path from one of the sources to that node. If target is not None, returns a tuple of (distance, path) where distance is the distance from source to target and path is a list representing the path from source to target.

Raises:
NodeNotFound

If `source` is not in `G`.

Notes

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

Examples

```>>> G = nx.path_graph(5)
>>> length, path = nx.single_source_bellman_ford(G, 0)
>>> length[4]
4
>>> for node in [0, 1, 2, 3, 4]:
...     print(f"{node}: {length[node]}")
0: 0
1: 1
2: 2
3: 3
4: 4
>>> path[4]
[0, 1, 2, 3, 4]
>>> length, path = nx.single_source_bellman_ford(G, 0, 1)
>>> length
1
>>> path
[0, 1]
```

Additional backends implement this function

cugraphGPU-accelerated backend.

Negative cycles are not yet supported. `NotImplementedError` will be raised if there are negative edge weights. We plan to support negative edge weights soon. Also, callable `weight` argument is not supported.

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.