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# single_source_bellman_ford

single_source_bellman_ford(G, source, target=None, weight='weight')

  Compute shortest paths and lengths in a weighted graph G.

  Uses Bellman-Ford algorithm for shortest paths.

  Parameters:
    G NetworkX graph
    source node label

      Starting node for path

    target node label, optional

      Ending node for path

    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.

  Returns:
    distance, path pair 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`.

  See also

  `single_source_dijkstra`
  `single_source_bellman_ford_path`
  `single_source_bellman_ford_path_length`

  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]