All-to-One Shortest Distances on Directed Graph

BELLMAN_FORD, a Python library which implements the Bellman-Ford algorithm for finding the shortest distance from a given node to all other nodes in a directed graph whose edges have been assigned real-valued lengths.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


BELLMAN_FORD is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

DIJKSTRA, a Python library which implements a simple version of Dijkstra's minimum distance algorithm for graphs.

TOMS097, a Python library which computes the distance between all pairs of nodes in a directed graph with weighted edges, using Floyd's algorithm.


  1. Richard Bellman,
    On a routing problem,
    Quarterly of Applied Mathematics,
    Volume 16, 1958, pages 87-90.
  2. Lester Ford,
    Network Flow Theory,
    RAND Corporation Paper P-923, 1956.

Source Code:

Examples and Tests:

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Last revised on 13 November 2014.