goldberg_radzik(G, source, weight='weight')
The algorithm has a running time of $O(mn)$ where $n$ is the number of nodes and $m$ is the number of edges. It is slower than Dijkstra but can handle negative edge weights.
Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.
The dictionaries returned only have keys for nodes reachable from the source.
In the case where the (di)graph is not connected, if a component not containing the source contains a negative (di)cycle, it will not be detected.
The algorithm works for all types of graphs, including directed graphs and multigraphs.
Starting node for path
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 :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 :None:None:`source` is not in G.
If the (di)graph contains a negative (di)cycle, the algorithm raises an exception to indicate the presence of the negative (di)cycle. Note: any negative weight edge in an undirected graph is a negative cycle.
Returns two dictionaries keyed by node to predecessor in the path and to the distance from the source respectively.
Compute shortest path lengths and predecessors on shortest paths in weighted graphs.
>>> G = nx.path_graph(5, create_using=nx.DiGraph())
... pred, dist = nx.goldberg_radzik(G, 0)
... sorted(pred.items()) [(0, None), (1, 0), (2, 1), (3, 2), (4, 3)]
>>> sorted(dist.items()) [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)]This example is valid syntax, but raise an exception at execution
>>> G = nx.cycle_graph(5, create_using=nx.DiGraph())See :
... G[1][2]["weight"] = -7
... nx.goldberg_radzik(G, 0) Traceback (most recent call last): ... networkx.exception.NetworkXUnbounded: Negative cycle detected.
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.shortest_paths.weighted.goldberg_radzik
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