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johnson¶

johnson
(G, weight='weight')[source]¶ Compute shortest paths between all nodes in a weighted graph using Johnson’s algorithm.
Parameters:  G (NetworkX graph) –
 weight (string, optional (default=’weight’)) – Edge data key corresponding to the edge weight.
Returns: distance – Dictionary, keyed by source and target, of shortest paths.
Return type: dictionary
Raises: NetworkXError
– If given graph is not weighted.Examples
>>> import networkx as nx >>> graph = nx.DiGraph() >>> graph.add_weighted_edges_from([('0', '3', 3), ('0', '1', 5), ... ('0', '2', 2), ('1', '2', 4), ('2', '3', 1)]) >>> paths = nx.johnson(graph, weight='weight') >>> paths['0']['2'] ['0', '1', '2']
Johnson’s algorithm is suitable even for graphs with negative weights. It works by using the Bellman–Ford algorithm to compute a transformation of the input graph that removes all negative weights, allowing Dijkstra’s algorithm to be used on the transformed graph.
It may be faster than Floyd  Warshall algorithm in sparse graphs. Algorithm complexity: O(V^2 * logV + V * E)
See also
floyd_warshall_predecessor_and_distance()
,floyd_warshall_numpy()
,all_pairs_shortest_path()
,all_pairs_shortest_path_length()
,all_pairs_dijkstra_path()
,bellman_ford()