floyd_warshall_successor_and_distance(graph, weight_fn=None, default_weight=1.0, parallel_threshold=300)[source]#

Find all-pairs shortest path lengths using Floyd’s algorithm.

Floyd’s algorithm is used for finding shortest paths in dense graphs or graphs with negative weights (where Dijkstra’s algorithm fails).

This function is multithreaded and will launch a pool with threads equal to the number of CPUs by default if the number of nodes in the graph is above the value of parallel_threshold (it defaults to 300). You can tune the number of threads with the RAYON_NUM_THREADS environment variable. For example, setting RAYON_NUM_THREADS=4 would limit the thread pool to 4 threads if parallelization was enabled.

  • graph (PyDiGraph) – The directed graph to run Floyd’s algorithm on

  • weight_fn

    A callable object (function, lambda, etc) which will be passed the edge object and expected to return a float. This tells rustworkx/rust how to extract a numerical weight as a float for edge object. Some simple examples are:

    floyd_warshall_successor_and_distance(graph, weight_fn=lambda _: 1)

    to return a weight of 1 for all edges. Also:

    floyd_warshall_successor_and_distance(graph, weight_fn=float)

    to cast the edge object as a float as the weight.

  • as_undirected – If set to true each directed edge will be treated as bidirectional/undirected.

  • parallel_threshold (int) – The number of nodes to execute the algorithm in parallel at. It defaults to 300, but this can be tuned


A tuple of two matrices. First one is a matrix of shortest path distances between nodes. If there is no path between two nodes then the corresponding matrix entry will be np.inf. Second one is a matrix of next nodes for given source and target. If there is no path between two nodes then the corresponding matrix entry will be the same as a target node. To reconstruct the shortest path among nodes:

def reconstruct_path(source, target, successors):
    path = []
    if source == target:
        return path
    curr = source
    while curr != target:
        curr = successors[curr, target]
    return path

Return type:

(numpy.ndarray, numpy.ndarray)