🕷️ Crawler Inspector

[Skip to main content](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.bellman_ford.html#main-content) Back to top [  SciPy](https://docs.scipy.org/doc/scipy/index.html) - [Installing](https://scipy.org/install/) - [User Guide](https://docs.scipy.org/doc/scipy/tutorial/index.html) - [API reference](https://docs.scipy.org/doc/scipy/reference/index.html) - [Building from source](https://docs.scipy.org/doc/scipy/building/index.html) - [Development](https://docs.scipy.org/doc/scipy/dev/index.html) - [Release notes](https://docs.scipy.org/doc/scipy/release.html) Choose version - [GitHub](https://github.com/scipy/scipy "GitHub") - [Scientific Python Forum](https://discuss.scientific-python.org/c/contributor/scipy/ "Scientific Python Forum") - [Installing](https://scipy.org/install/) - [User Guide](https://docs.scipy.org/doc/scipy/tutorial/index.html) - [API reference](https://docs.scipy.org/doc/scipy/reference/index.html) - [Building from source](https://docs.scipy.org/doc/scipy/building/index.html) - [Development](https://docs.scipy.org/doc/scipy/dev/index.html) - [Release notes](https://docs.scipy.org/doc/scipy/release.html) Choose version - [GitHub](https://github.com/scipy/scipy "GitHub") - [Scientific Python Forum](https://discuss.scientific-python.org/c/contributor/scipy/ "Scientific Python Forum") Search `Ctrl`\+`K` Section Navigation - [scipy](https://docs.scipy.org/doc/scipy/reference/main_namespace.html) - [scipy.cluster](https://docs.scipy.org/doc/scipy/reference/cluster.html) - [scipy.constants](https://docs.scipy.org/doc/scipy/reference/constants.html) - [scipy.datasets](https://docs.scipy.org/doc/scipy/reference/datasets.html) - [scipy.differentiate](https://docs.scipy.org/doc/scipy/reference/differentiate.html) - [scipy.fft](https://docs.scipy.org/doc/scipy/reference/fft.html) - [scipy.fftpack](https://docs.scipy.org/doc/scipy/reference/fftpack.html) - [scipy.integrate](https://docs.scipy.org/doc/scipy/reference/integrate.html) - [scipy.interpolate](https://docs.scipy.org/doc/scipy/reference/interpolate.html) - [scipy.io](https://docs.scipy.org/doc/scipy/reference/io.html) - [scipy.linalg](https://docs.scipy.org/doc/scipy/reference/linalg.html) - [scipy.ndimage](https://docs.scipy.org/doc/scipy/reference/ndimage.html) - [scipy.odr](https://docs.scipy.org/doc/scipy/reference/odr.html) - [scipy.optimize](https://docs.scipy.org/doc/scipy/reference/optimize.html) - [scipy.signal](https://docs.scipy.org/doc/scipy/reference/signal.html) - [scipy.sparse](https://docs.scipy.org/doc/scipy/reference/sparse.html) - [scipy.spatial](https://docs.scipy.org/doc/scipy/reference/spatial.html) - [scipy.special](https://docs.scipy.org/doc/scipy/reference/special.html) - [scipy.stats](https://docs.scipy.org/doc/scipy/reference/stats.html) - [SciPy API](https://docs.scipy.org/doc/scipy/reference/index.html) - [Sparse arrays (`scipy.sparse`)](https://docs.scipy.org/doc/scipy/reference/sparse.html) - [Compressed sparse graph routines (`scipy.sparse.csgraph`)](https://docs.scipy.org/doc/scipy/reference/sparse.csgraph.html) - bellman\_ford scipy.sparse.csgraph. # bellman\_ford[\#](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.bellman_ford.html#bellman-ford "Link to this heading") scipy.sparse.csgraph.bellman\_ford(*csgraph*, *directed\=True*, *indices\=None*, *return\_predecessors\=False*, *unweighted\=False*)[\#](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.bellman_ford.html#scipy.sparse.csgraph.bellman_ford "Link to this definition") Compute the shortest path lengths using the Bellman-Ford algorithm. The Bellman-Ford algorithm can robustly deal with graphs with negative weights. If a negative cycle is detected, an error is raised. For graphs without negative edge weights, Dijkstra’s algorithm may be faster. Added in version 0.11.0. Parameters: **csgraph**array\_like, or sparse array or matrix, 2 dimensions The N x N array of distances representing the input graph. **directed**bool, optional If True (default), then find the shortest path on a directed graph: only move from point i to point j along paths csgraph\[i, j\]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph\[i, j\] or csgraph\[j, i\] **indices**array\_like or int, optional if specified, only compute the paths from the points at the given indices. **return\_predecessors**bool, optional If True, return the size (N, N) predecessor matrix. **unweighted**bool, optional If True, then find unweighted distances. That is, rather than finding the path between each point such that the sum of weights is minimized, find the path such that the number of edges is minimized. Returns: **dist\_matrix**ndarray The N x N matrix of distances between graph nodes. dist\_matrix\[i,j\] gives the shortest distance from point i to point j along the graph. **predecessors**ndarray, shape (n\_indices, n\_nodes,) Returned only if `return_predecessors=True`. If *indices* is None then `n_indices = n_nodes` and the shape of the matrix becomes `(n_nodes, n_nodes)`. The matrix of predecessors, which can be used to reconstruct the shortest paths. Row i of the predecessor matrix contains information on the shortest paths from point i: each entry predecessors\[i, j\] gives the index of the previous node in the path from point i to point j. If no path exists between point i and j, then predecessors\[i, j\] = -9999 Raises: NegativeCycleError: if there are negative cycles in the graph Notes This routine is specially designed for graphs with negative edge weights. If all edge weights are positive, then Dijkstra’s algorithm is a better choice. If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples Try it in your browser\! ``` >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import bellman_ford ``` ``` >>> graph = [ ... [0, 1 ,2, 0], ... [0, 0, 0, 1], ... [2, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> graph = csr_array(graph) >>> print(graph) <Compressed Sparse Row sparse array of dtype 'int64' with 5 stored elements and shape (4, 4)> Coords Values (0, 1) 1 (0, 2) 2 (1, 3) 1 (2, 0) 2 (2, 3) 3 ``` ``` >>> dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True) >>> dist_matrix array([0., 1., 2., 2.]) >>> predecessors array([-9999, 0, 0, 1], dtype=int32) ``` Go Back Open In Tab [previous floyd\_warshall](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.floyd_warshall.html "previous page") [next johnson](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.johnson.html "next page") On this page - [`bellman_ford`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.bellman_ford.html#scipy.sparse.csgraph.bellman_ford) © Copyright 2008, The SciPy community. Created using [Sphinx](https://www.sphinx-doc.org/) 8.1.3. Built with the [PyData Sphinx Theme](https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html) 0.16.1.

scipy.sparse.csgraph. scipy.sparse.csgraph.bellman\_ford(*csgraph*, *directed\=True*, *indices\=None*, *return\_predecessors\=False*, *unweighted\=False*)[\#](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.bellman_ford.html#scipy.sparse.csgraph.bellman_ford "Link to this definition") Compute the shortest path lengths using the Bellman-Ford algorithm. The Bellman-Ford algorithm can robustly deal with graphs with negative weights. If a negative cycle is detected, an error is raised. For graphs without negative edge weights, Dijkstra’s algorithm may be faster. Added in version 0.11.0. Parameters: **csgraph**array\_like, or sparse array or matrix, 2 dimensions The N x N array of distances representing the input graph. **directed**bool, optional If True (default), then find the shortest path on a directed graph: only move from point i to point j along paths csgraph\[i, j\]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph\[i, j\] or csgraph\[j, i\] **indices**array\_like or int, optional if specified, only compute the paths from the points at the given indices. **return\_predecessors**bool, optional If True, return the size (N, N) predecessor matrix. **unweighted**bool, optional If True, then find unweighted distances. That is, rather than finding the path between each point such that the sum of weights is minimized, find the path such that the number of edges is minimized. Returns: **dist\_matrix**ndarray The N x N matrix of distances between graph nodes. dist\_matrix\[i,j\] gives the shortest distance from point i to point j along the graph. **predecessors**ndarray, shape (n\_indices, n\_nodes,) Returned only if `return_predecessors=True`. If *indices* is None then `n_indices = n_nodes` and the shape of the matrix becomes `(n_nodes, n_nodes)`. The matrix of predecessors, which can be used to reconstruct the shortest paths. Row i of the predecessor matrix contains information on the shortest paths from point i: each entry predecessors\[i, j\] gives the index of the previous node in the path from point i to point j. If no path exists between point i and j, then predecessors\[i, j\] = -9999 Raises: NegativeCycleError: if there are negative cycles in the graph Notes This routine is specially designed for graphs with negative edge weights. If all edge weights are positive, then Dijkstra’s algorithm is a better choice. If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples ``` >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import bellman_ford ``` ``` >>> graph = [ ... [0, 1 ,2, 0], ... [0, 0, 0, 1], ... [2, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> graph = csr_array(graph) >>> print(graph) <Compressed Sparse Row sparse array of dtype 'int64' with 5 stored elements and shape (4, 4)> Coords Values (0, 1) 1 (0, 2) 2 (1, 3) 1 (2, 0) 2 (2, 3) 3 ``` ``` >>> dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True) >>> dist_matrix array([0., 1., 2., 2.]) >>> predecessors array([-9999, 0, 0, 1], dtype=int32) ```