- johnson(G, weight='weight')¶
Uses Johnson’s Algorithm to compute shortest paths.
Johnson’s Algorithm finds a shortest path between each pair of nodes in a weighted graph even if negative weights are present.
- GNetworkX graph
- weightstring 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
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.
Dictionary, keyed by source and target, of shortest paths.
If given graph is not weighted.
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.
The time complexity of this algorithm is \(O(n^2 \log n + n m)\), where \(n\) is the number of nodes and \(m\) the number of edges in the graph. For dense graphs, this may be faster than the Floyd–Warshall algorithm.
>>> 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']