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# dijkstra_predecessor_and_distance

dijkstra_predecessor_and_distance(G, source, cutoff=None, weight='weight')

  Compute weighted shortest path length and predecessors.

  Uses Dijkstra’s Method to obtain the shortest weighted paths and return dictionaries of predecessors for each node and distance for each node from the `source`.

  Parameters:
    G NetworkX graph
    source node label

      Starting 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:
    pred, distance dictionaries

      Returns two dictionaries representing a list of predecessors of a node and the distance to each node.

  Raises:
    NodeNotFound

      If `source` is not in `G`.

  Notes

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

  The list of predecessors contains more than one element only when there are more than one shortest paths to the key node.

  Examples

      >>> G = nx.path_graph(5, create_using=nx.DiGraph())
      >>> pred, dist = nx.dijkstra_predecessor_and_distance(G, 0)
      >>> sorted(pred.items())
      [(0, []), (1, [0]), (2, [1]), (3, [2]), (4, [3])]
      >>> sorted(dist.items())
      [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)]

      >>> pred, dist = nx.dijkstra_predecessor_and_distance(G, 0, 1)
      >>> sorted(pred.items())
      [(0, []), (1, [0])]
      >>> sorted(dist.items())
      [(0, 0), (1, 1)]