bw_graph_tools.shortest_path

Created on November 12, 2019 @author: Quentin Lutz <qlutz@enst.fr> From scikit-network version 0.30

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Copyright (c) 2018, Scikit-network Developers Bertrand Charpentier <bertrand.charpentier@live.fr> Thomas Bonald <thomas.bonald@telecom-paristech.fr> All rights reserved.

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Functions

get_distances(adjacency[, sources, method, ...])

Compute distances between nodes.

get_shortest_path(adjacency, sources, targets[, ...])

Compute the shortest paths in the graph.

Module Contents

bw_graph_tools.shortest_path.get_distances(adjacency: scipy.sparse.csr_matrix, sources: int | Iterable | None = None, method: str = 'D', return_predecessors: bool = False, unweighted: bool = False, n_jobs: int | None = None)[source]

Compute distances between nodes.

  • Graphs

  • Digraphs

Based on SciPy (scipy.sparse.csgraph.shortest_path)

Parameters:

  • adjacency – The adjacency matrix of the graph

  • sources – If specified, only compute the paths for the points at the given indices. Will not work with method =='FW'.

  • method –

    The method to be used.

    • 'D' (Dijkstra),

    • 'BF' (Bellman-Ford),

    • 'J' (Johnson).

  • return_predecessors – If True, the size predecessor matrix is returned

  • unweighted – If True, the weights of the edges are ignored

  • n_jobs – If an integer value is given, denotes the number of workers to use (-1 means the maximum number will be used). If None, no parallel computations are made.

Returns:

  • dist_matrix (np.ndarray) – Matrix of distances between nodes. dist_matrix[i,j] gives the shortest distance from the i-th source to node j in the graph (infinite if no path exists from the i-th source to node j).

  • predecessors (np.ndarray, optional) – Returned only if return_predecessors == True. 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 the i-th source: each entry predecessors[i, j] gives the index of the previous node in the path from the i-th source to node j (-1 if no path exists from the i-th source to node j).

bw_graph_tools.shortest_path.get_shortest_path(adjacency: scipy.sparse.csr_matrix, sources: int | Iterable, targets: int | Iterable, method: str = 'D', unweighted: bool = False, n_jobs: int | None = None)[source]

Compute the shortest paths in the graph.

Parameters:

  • adjacency – The adjacency matrix of the graph

  • sources (int or iterable) – Sources nodes.

  • targets (int or iterable) – Target nodes.

  • method –

    The method to be used.

    • 'D' (Dijkstra),

    • 'BF' (Bellman-Ford),

    • 'J' (Johnson).

  • unweighted – If True, the weights of the edges are ignored

  • n_jobs – If an integer value is given, denotes the number of workers to use (-1 means the maximum number will be used). If None, no parallel computations are made.

Returns:

paths – If single source and single target, return a list containing the nodes on the path from source to target. If multiple sources or multiple targets, return a list of paths as lists. An empty list means that the path does not exist.

Return type:

list

Examples

>>> from sknetwork.data import linear_digraph
>>> adjacency = linear_digraph(3)
>>> get_shortest_path(adjacency, 0, 2)
[0, 1, 2]
>>> get_shortest_path(adjacency, 2, 0)
[]
>>> get_shortest_path(adjacency, 0, [1, 2])
[[0, 1], [0, 1, 2]]
>>> get_shortest_path(adjacency, [0, 1], 2)
[[0, 1, 2], [1, 2]]