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# multi_source_dijkstra

multi_source_dijkstra(G, sources, target=None, cutoff=None, weight='weight')

  Find shortest weighted paths and lengths from a given set of source nodes.

  Uses Dijkstra’s algorithm to compute the shortest paths and lengths between one of the source nodes and the given `target`, or all other reachable nodes if not specified, 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.

    target node label, optional

      Ending node for path

    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:
    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:
    ValueError

      If `sources` is empty.

    NodeNotFound

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

  See also

  `multi_source_dijkstra_path`
  `multi_source_dijkstra_path_length`

  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.

  Based on the Python cookbook recipe (119466) at https://code.activestate.com/recipes/119466/

  This algorithm is not guaranteed to work if edge weights are negative or are floating point numbers (overflows and roundoff errors can cause problems).

  Examples

      >>> G = nx.path_graph(5)
      >>> length, path = nx.multi_source_dijkstra(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
      >>> path[1]
      [0, 1]
      >>> path[3]
      [4, 3]

      >>> length, path = nx.multi_source_dijkstra(G, {0, 4}, 1)
      >>> length
      1
      >>> path
      [0, 1]