# networkx.algorithms.shortest_paths.weighted.dijkstra_predecessor_and_distance¶

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

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) – Depth to stop the search. Only return paths with length <= 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.

Returns

pred, distance – Returns two dictionaries representing a list of predecessors of a node and the distance to each node. Warning: If target is specified, the dicts are incomplete as they only contain information for the nodes along a path to target.

Return type

dictionaries

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, ), (2, ), (3, ), (4, )]
>>> 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, )]
>>> sorted(dist.items())
[(0, 0), (1, 1)]