johnson(G, weight='weight')
Johnson's Algorithm finds a shortest path between each pair of nodes in a weighted graph even if negative weights are present.
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.
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 :None:None:`u` to :None:None:`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.
If given graph is not weighted.
Dictionary, keyed by source and target, of shortest paths.
Uses Johnson's Algorithm to compute shortest paths.
>>> graph = nx.DiGraph()See :
... 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']
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.shortest_paths.weighted.johnson
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them