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# multi_source_dijkstra_path_length

multi_source_dijkstra_path_length(G, sources, cutoff=None, weight='weight')

  Find shortest weighted path lengths in G from a given set of source nodes.

  Compute the shortest path length between any of the source nodes and all other reachable nodes for a weighted graph.

  Parameters:
    G NetworkX graph
    sources non-empty set of nodes

      Starting nodes for paths. If this is just a set containing a single node, then all paths computed by this function will start from that node. If there are two or more nodes in the set, the computed paths may begin from any one of the start nodes.

    cutoff integer 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.

    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 or None to indicate a hidden edge.

  Returns:
    length dict

      Dict keyed by node to shortest path length to nearest source.

  Raises:
    ValueError

      If `sources` is empty.

    NodeNotFound

      If any of `sources` is not in `G`.

  See also

  `multi_source_dijkstra`

  Notes

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

  The weight function can be used to hide edges by returning None. So `weight = lambda u, v, d: 1 if d['color']=="red" else None` will find the shortest red path.

  Examples

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