965 lines
30 KiB
Python
965 lines
30 KiB
Python
from heapq import heappop, heappush
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from itertools import count
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import networkx as nx
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from networkx.algorithms.shortest_paths.weighted import _weight_function
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from networkx.utils import not_implemented_for, pairwise
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__all__ = [
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"all_simple_paths",
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"is_simple_path",
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"shortest_simple_paths",
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"all_simple_edge_paths",
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]
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def is_simple_path(G, nodes):
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"""Returns True if and only if `nodes` form a simple path in `G`.
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A *simple path* in a graph is a nonempty sequence of nodes in which
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no node appears more than once in the sequence, and each adjacent
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pair of nodes in the sequence is adjacent in the graph.
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Parameters
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----------
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G : graph
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A NetworkX graph.
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nodes : list
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A list of one or more nodes in the graph `G`.
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Returns
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-------
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bool
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Whether the given list of nodes represents a simple path in `G`.
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Notes
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-----
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An empty list of nodes is not a path but a list of one node is a
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path. Here's an explanation why.
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This function operates on *node paths*. One could also consider
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*edge paths*. There is a bijection between node paths and edge
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paths.
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The *length of a path* is the number of edges in the path, so a list
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of nodes of length *n* corresponds to a path of length *n* - 1.
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Thus the smallest edge path would be a list of zero edges, the empty
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path. This corresponds to a list of one node.
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To convert between a node path and an edge path, you can use code
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like the following::
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>>> from networkx.utils import pairwise
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>>> nodes = [0, 1, 2, 3]
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>>> edges = list(pairwise(nodes))
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>>> edges
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[(0, 1), (1, 2), (2, 3)]
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>>> nodes = [edges[0][0]] + [v for u, v in edges]
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>>> nodes
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[0, 1, 2, 3]
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Examples
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--------
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>>> G = nx.cycle_graph(4)
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>>> nx.is_simple_path(G, [2, 3, 0])
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True
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>>> nx.is_simple_path(G, [0, 2])
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False
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"""
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# The empty list is not a valid path. Could also return
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# NetworkXPointlessConcept here.
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if len(nodes) == 0:
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return False
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# If the list is a single node, just check that the node is actually
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# in the graph.
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if len(nodes) == 1:
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return nodes[0] in G
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# Test that no node appears more than once, and that each
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# adjacent pair of nodes is adjacent.
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return len(set(nodes)) == len(nodes) and all(v in G[u] for u, v in pairwise(nodes))
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def all_simple_paths(G, source, target, cutoff=None):
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"""Generate all simple paths in the graph G from source to target.
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A simple path is a path with no repeated nodes.
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Parameters
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----------
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G : NetworkX graph
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source : node
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Starting node for path
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target : nodes
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Single node or iterable of nodes at which to end path
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cutoff : integer, optional
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Depth to stop the search. Only paths of length <= cutoff are returned.
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Returns
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-------
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path_generator: generator
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A generator that produces lists of simple paths. If there are no paths
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between the source and target within the given cutoff the generator
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produces no output. If it is possible to traverse the same sequence of
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nodes in multiple ways, namely through parallel edges, then it will be
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returned multiple times (once for each viable edge combination).
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Examples
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--------
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This iterator generates lists of nodes::
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>>> G = nx.complete_graph(4)
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>>> for path in nx.all_simple_paths(G, source=0, target=3):
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... print(path)
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...
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[0, 1, 2, 3]
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[0, 1, 3]
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[0, 2, 1, 3]
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[0, 2, 3]
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[0, 3]
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You can generate only those paths that are shorter than a certain
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length by using the `cutoff` keyword argument::
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>>> paths = nx.all_simple_paths(G, source=0, target=3, cutoff=2)
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>>> print(list(paths))
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[[0, 1, 3], [0, 2, 3], [0, 3]]
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To get each path as the corresponding list of edges, you can use the
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:func:`networkx.utils.pairwise` helper function::
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>>> paths = nx.all_simple_paths(G, source=0, target=3)
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>>> for path in map(nx.utils.pairwise, paths):
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... print(list(path))
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[(0, 1), (1, 2), (2, 3)]
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[(0, 1), (1, 3)]
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[(0, 2), (2, 1), (1, 3)]
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[(0, 2), (2, 3)]
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[(0, 3)]
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Pass an iterable of nodes as target to generate all paths ending in any of several nodes::
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>>> G = nx.complete_graph(4)
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>>> for path in nx.all_simple_paths(G, source=0, target=[3, 2]):
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... print(path)
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...
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[0, 1, 2]
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[0, 1, 2, 3]
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[0, 1, 3]
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[0, 1, 3, 2]
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[0, 2]
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[0, 2, 1, 3]
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[0, 2, 3]
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[0, 3]
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[0, 3, 1, 2]
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[0, 3, 2]
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Iterate over each path from the root nodes to the leaf nodes in a
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directed acyclic graph using a functional programming approach::
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>>> from itertools import chain
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>>> from itertools import product
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>>> from itertools import starmap
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>>> from functools import partial
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>>>
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>>> chaini = chain.from_iterable
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>>>
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>>> G = nx.DiGraph([(0, 1), (1, 2), (0, 3), (3, 2)])
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>>> roots = (v for v, d in G.in_degree() if d == 0)
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>>> leaves = (v for v, d in G.out_degree() if d == 0)
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>>> all_paths = partial(nx.all_simple_paths, G)
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>>> list(chaini(starmap(all_paths, product(roots, leaves))))
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[[0, 1, 2], [0, 3, 2]]
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The same list computed using an iterative approach::
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>>> G = nx.DiGraph([(0, 1), (1, 2), (0, 3), (3, 2)])
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>>> roots = (v for v, d in G.in_degree() if d == 0)
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>>> leaves = (v for v, d in G.out_degree() if d == 0)
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>>> all_paths = []
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>>> for root in roots:
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... for leaf in leaves:
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... paths = nx.all_simple_paths(G, root, leaf)
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... all_paths.extend(paths)
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>>> all_paths
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[[0, 1, 2], [0, 3, 2]]
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Iterate over each path from the root nodes to the leaf nodes in a
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directed acyclic graph passing all leaves together to avoid unnecessary
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compute::
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>>> G = nx.DiGraph([(0, 1), (2, 1), (1, 3), (1, 4)])
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>>> roots = (v for v, d in G.in_degree() if d == 0)
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>>> leaves = [v for v, d in G.out_degree() if d == 0]
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>>> all_paths = []
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>>> for root in roots:
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... paths = nx.all_simple_paths(G, root, leaves)
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... all_paths.extend(paths)
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>>> all_paths
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[[0, 1, 3], [0, 1, 4], [2, 1, 3], [2, 1, 4]]
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If parallel edges offer multiple ways to traverse a given sequence of
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nodes, this sequence of nodes will be returned multiple times:
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>>> G = nx.MultiDiGraph([(0, 1), (0, 1), (1, 2)])
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>>> list(nx.all_simple_paths(G, 0, 2))
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[[0, 1, 2], [0, 1, 2]]
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Notes
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-----
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This algorithm uses a modified depth-first search to generate the
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paths [1]_. A single path can be found in $O(V+E)$ time but the
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number of simple paths in a graph can be very large, e.g. $O(n!)$ in
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the complete graph of order $n$.
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This function does not check that a path exists between `source` and
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`target`. For large graphs, this may result in very long runtimes.
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Consider using `has_path` to check that a path exists between `source` and
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`target` before calling this function on large graphs.
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References
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----------
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.. [1] R. Sedgewick, "Algorithms in C, Part 5: Graph Algorithms",
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Addison Wesley Professional, 3rd ed., 2001.
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See Also
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--------
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all_shortest_paths, shortest_path, has_path
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"""
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if source not in G:
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raise nx.NodeNotFound(f"source node {source} not in graph")
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if target in G:
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targets = {target}
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else:
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try:
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targets = set(target)
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except TypeError as err:
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raise nx.NodeNotFound(f"target node {target} not in graph") from err
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if source in targets:
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return _empty_generator()
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if cutoff is None:
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cutoff = len(G) - 1
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if cutoff < 1:
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return _empty_generator()
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if G.is_multigraph():
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return _all_simple_paths_multigraph(G, source, targets, cutoff)
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else:
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return _all_simple_paths_graph(G, source, targets, cutoff)
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def _empty_generator():
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yield from ()
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def _all_simple_paths_graph(G, source, targets, cutoff):
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visited = dict.fromkeys([source])
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stack = [iter(G[source])]
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while stack:
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children = stack[-1]
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child = next(children, None)
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if child is None:
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stack.pop()
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visited.popitem()
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elif len(visited) < cutoff:
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if child in visited:
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continue
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if child in targets:
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yield list(visited) + [child]
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visited[child] = None
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if targets - set(visited.keys()): # expand stack until find all targets
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stack.append(iter(G[child]))
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else:
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visited.popitem() # maybe other ways to child
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else: # len(visited) == cutoff:
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for target in (targets & (set(children) | {child})) - set(visited.keys()):
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yield list(visited) + [target]
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stack.pop()
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visited.popitem()
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def _all_simple_paths_multigraph(G, source, targets, cutoff):
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visited = dict.fromkeys([source])
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stack = [(v for u, v in G.edges(source))]
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while stack:
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children = stack[-1]
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child = next(children, None)
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if child is None:
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stack.pop()
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visited.popitem()
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elif len(visited) < cutoff:
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if child in visited:
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continue
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if child in targets:
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yield list(visited) + [child]
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visited[child] = None
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if targets - set(visited.keys()):
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stack.append((v for u, v in G.edges(child)))
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else:
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visited.popitem()
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else: # len(visited) == cutoff:
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for target in targets - set(visited.keys()):
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count = ([child] + list(children)).count(target)
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for i in range(count):
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yield list(visited) + [target]
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stack.pop()
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visited.popitem()
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def all_simple_edge_paths(G, source, target, cutoff=None):
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"""Generate lists of edges for all simple paths in G from source to target.
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A simple path is a path with no repeated nodes.
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Parameters
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----------
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G : NetworkX graph
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source : node
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Starting node for path
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target : nodes
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Single node or iterable of nodes at which to end path
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cutoff : integer, optional
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Depth to stop the search. Only paths of length <= cutoff are returned.
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Returns
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-------
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path_generator: generator
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A generator that produces lists of simple paths. If there are no paths
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between the source and target within the given cutoff the generator
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produces no output.
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For multigraphs, the list of edges have elements of the form `(u,v,k)`.
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Where `k` corresponds to the edge key.
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Examples
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--------
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Print the simple path edges of a Graph::
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>>> g = nx.Graph([(1, 2), (2, 4), (1, 3), (3, 4)])
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>>> for path in sorted(nx.all_simple_edge_paths(g, 1, 4)):
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... print(path)
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[(1, 2), (2, 4)]
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[(1, 3), (3, 4)]
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Print the simple path edges of a MultiGraph. Returned edges come with
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their associated keys::
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>>> mg = nx.MultiGraph()
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>>> mg.add_edge(1, 2, key="k0")
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'k0'
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>>> mg.add_edge(1, 2, key="k1")
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'k1'
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>>> mg.add_edge(2, 3, key="k0")
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'k0'
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>>> for path in sorted(nx.all_simple_edge_paths(mg, 1, 3)):
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... print(path)
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[(1, 2, 'k0'), (2, 3, 'k0')]
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[(1, 2, 'k1'), (2, 3, 'k0')]
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Notes
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-----
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This algorithm uses a modified depth-first search to generate the
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paths [1]_. A single path can be found in $O(V+E)$ time but the
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number of simple paths in a graph can be very large, e.g. $O(n!)$ in
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the complete graph of order $n$.
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References
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----------
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.. [1] R. Sedgewick, "Algorithms in C, Part 5: Graph Algorithms",
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Addison Wesley Professional, 3rd ed., 2001.
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See Also
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--------
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all_shortest_paths, shortest_path, all_simple_paths
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"""
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if source not in G:
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raise nx.NodeNotFound("source node %s not in graph" % source)
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if target in G:
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targets = {target}
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else:
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try:
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targets = set(target)
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except TypeError:
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raise nx.NodeNotFound("target node %s not in graph" % target)
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if source in targets:
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return []
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if cutoff is None:
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cutoff = len(G) - 1
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if cutoff < 1:
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return []
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if G.is_multigraph():
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for simp_path in _all_simple_edge_paths_multigraph(G, source, targets, cutoff):
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yield simp_path
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else:
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for simp_path in _all_simple_paths_graph(G, source, targets, cutoff):
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yield list(zip(simp_path[:-1], simp_path[1:]))
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def _all_simple_edge_paths_multigraph(G, source, targets, cutoff):
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if not cutoff or cutoff < 1:
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return []
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visited = [source]
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stack = [iter(G.edges(source, keys=True))]
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while stack:
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children = stack[-1]
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child = next(children, None)
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if child is None:
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stack.pop()
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visited.pop()
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elif len(visited) < cutoff:
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if child[1] in targets:
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yield visited[1:] + [child]
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elif child[1] not in [v[0] for v in visited[1:]]:
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visited.append(child)
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stack.append(iter(G.edges(child[1], keys=True)))
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else: # len(visited) == cutoff:
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for (u, v, k) in [child] + list(children):
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if v in targets:
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yield visited[1:] + [(u, v, k)]
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stack.pop()
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visited.pop()
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@not_implemented_for("multigraph")
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def shortest_simple_paths(G, source, target, weight=None):
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"""Generate all simple paths in the graph G from source to target,
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starting from shortest ones.
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A simple path is a path with no repeated nodes.
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If a weighted shortest path search is to be used, no negative weights
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are allowed.
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Parameters
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----------
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G : NetworkX graph
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source : node
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Starting node for path
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target : node
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Ending node for path
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weight : string or function
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If it is a string, it is the name of the edge attribute to be
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used as a weight.
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If it is a function, the weight of an edge is the value returned
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by the function. The function must accept exactly three positional
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arguments: the two endpoints of an edge and the dictionary of edge
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attributes for that edge. The function must return a number.
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If None all edges are considered to have unit weight. Default
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value None.
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Returns
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-------
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path_generator: generator
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A generator that produces lists of simple paths, in order from
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shortest to longest.
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Raises
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------
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NetworkXNoPath
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If no path exists between source and target.
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NetworkXError
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If source or target nodes are not in the input graph.
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NetworkXNotImplemented
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If the input graph is a Multi[Di]Graph.
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Examples
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--------
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>>> G = nx.cycle_graph(7)
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>>> paths = list(nx.shortest_simple_paths(G, 0, 3))
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>>> print(paths)
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[[0, 1, 2, 3], [0, 6, 5, 4, 3]]
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You can use this function to efficiently compute the k shortest/best
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paths between two nodes.
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>>> from itertools import islice
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>>> def k_shortest_paths(G, source, target, k, weight=None):
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... return list(
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... islice(nx.shortest_simple_paths(G, source, target, weight=weight), k)
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... )
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>>> for path in k_shortest_paths(G, 0, 3, 2):
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... print(path)
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[0, 1, 2, 3]
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[0, 6, 5, 4, 3]
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Notes
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-----
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This procedure is based on algorithm by Jin Y. Yen [1]_. Finding
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the first $K$ paths requires $O(KN^3)$ operations.
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See Also
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--------
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all_shortest_paths
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shortest_path
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all_simple_paths
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|
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References
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----------
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.. [1] Jin Y. Yen, "Finding the K Shortest Loopless Paths in a
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Network", Management Science, Vol. 17, No. 11, Theory Series
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(Jul., 1971), pp. 712-716.
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"""
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if source not in G:
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raise nx.NodeNotFound(f"source node {source} not in graph")
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if target not in G:
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raise nx.NodeNotFound(f"target node {target} not in graph")
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if weight is None:
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length_func = len
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shortest_path_func = _bidirectional_shortest_path
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else:
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wt = _weight_function(G, weight)
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|
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def length_func(path):
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|
return sum(
|
|
wt(u, v, G.get_edge_data(u, v)) for (u, v) in zip(path, path[1:])
|
|
)
|
|
|
|
shortest_path_func = _bidirectional_dijkstra
|
|
|
|
listA = list()
|
|
listB = PathBuffer()
|
|
prev_path = None
|
|
while True:
|
|
if not prev_path:
|
|
length, path = shortest_path_func(G, source, target, weight=weight)
|
|
listB.push(length, path)
|
|
else:
|
|
ignore_nodes = set()
|
|
ignore_edges = set()
|
|
for i in range(1, len(prev_path)):
|
|
root = prev_path[:i]
|
|
root_length = length_func(root)
|
|
for path in listA:
|
|
if path[:i] == root:
|
|
ignore_edges.add((path[i - 1], path[i]))
|
|
try:
|
|
length, spur = shortest_path_func(
|
|
G,
|
|
root[-1],
|
|
target,
|
|
ignore_nodes=ignore_nodes,
|
|
ignore_edges=ignore_edges,
|
|
weight=weight,
|
|
)
|
|
path = root[:-1] + spur
|
|
listB.push(root_length + length, path)
|
|
except nx.NetworkXNoPath:
|
|
pass
|
|
ignore_nodes.add(root[-1])
|
|
|
|
if listB:
|
|
path = listB.pop()
|
|
yield path
|
|
listA.append(path)
|
|
prev_path = path
|
|
else:
|
|
break
|
|
|
|
|
|
class PathBuffer:
|
|
def __init__(self):
|
|
self.paths = set()
|
|
self.sortedpaths = list()
|
|
self.counter = count()
|
|
|
|
def __len__(self):
|
|
return len(self.sortedpaths)
|
|
|
|
def push(self, cost, path):
|
|
hashable_path = tuple(path)
|
|
if hashable_path not in self.paths:
|
|
heappush(self.sortedpaths, (cost, next(self.counter), path))
|
|
self.paths.add(hashable_path)
|
|
|
|
def pop(self):
|
|
(cost, num, path) = heappop(self.sortedpaths)
|
|
hashable_path = tuple(path)
|
|
self.paths.remove(hashable_path)
|
|
return path
|
|
|
|
|
|
def _bidirectional_shortest_path(
|
|
G, source, target, ignore_nodes=None, ignore_edges=None, weight=None
|
|
):
|
|
"""Returns the shortest path between source and target ignoring
|
|
nodes and edges in the containers ignore_nodes and ignore_edges.
|
|
|
|
This is a custom modification of the standard bidirectional shortest
|
|
path implementation at networkx.algorithms.unweighted
|
|
|
|
Parameters
|
|
----------
|
|
G : NetworkX graph
|
|
|
|
source : node
|
|
starting node for path
|
|
|
|
target : node
|
|
ending node for path
|
|
|
|
ignore_nodes : container of nodes
|
|
nodes to ignore, optional
|
|
|
|
ignore_edges : container of edges
|
|
edges to ignore, optional
|
|
|
|
weight : None
|
|
This function accepts a weight argument for convenience of
|
|
shortest_simple_paths function. It will be ignored.
|
|
|
|
Returns
|
|
-------
|
|
path: list
|
|
List of nodes in a path from source to target.
|
|
|
|
Raises
|
|
------
|
|
NetworkXNoPath
|
|
If no path exists between source and target.
|
|
|
|
See Also
|
|
--------
|
|
shortest_path
|
|
|
|
"""
|
|
# call helper to do the real work
|
|
results = _bidirectional_pred_succ(G, source, target, ignore_nodes, ignore_edges)
|
|
pred, succ, w = results
|
|
|
|
# build path from pred+w+succ
|
|
path = []
|
|
# from w to target
|
|
while w is not None:
|
|
path.append(w)
|
|
w = succ[w]
|
|
# from source to w
|
|
w = pred[path[0]]
|
|
while w is not None:
|
|
path.insert(0, w)
|
|
w = pred[w]
|
|
|
|
return len(path), path
|
|
|
|
|
|
def _bidirectional_pred_succ(G, source, target, ignore_nodes=None, ignore_edges=None):
|
|
"""Bidirectional shortest path helper.
|
|
Returns (pred,succ,w) where
|
|
pred is a dictionary of predecessors from w to the source, and
|
|
succ is a dictionary of successors from w to the target.
|
|
"""
|
|
# does BFS from both source and target and meets in the middle
|
|
if ignore_nodes and (source in ignore_nodes or target in ignore_nodes):
|
|
raise nx.NetworkXNoPath(f"No path between {source} and {target}.")
|
|
if target == source:
|
|
return ({target: None}, {source: None}, source)
|
|
|
|
# handle either directed or undirected
|
|
if G.is_directed():
|
|
Gpred = G.predecessors
|
|
Gsucc = G.successors
|
|
else:
|
|
Gpred = G.neighbors
|
|
Gsucc = G.neighbors
|
|
|
|
# support optional nodes filter
|
|
if ignore_nodes:
|
|
|
|
def filter_iter(nodes):
|
|
def iterate(v):
|
|
for w in nodes(v):
|
|
if w not in ignore_nodes:
|
|
yield w
|
|
|
|
return iterate
|
|
|
|
Gpred = filter_iter(Gpred)
|
|
Gsucc = filter_iter(Gsucc)
|
|
|
|
# support optional edges filter
|
|
if ignore_edges:
|
|
if G.is_directed():
|
|
|
|
def filter_pred_iter(pred_iter):
|
|
def iterate(v):
|
|
for w in pred_iter(v):
|
|
if (w, v) not in ignore_edges:
|
|
yield w
|
|
|
|
return iterate
|
|
|
|
def filter_succ_iter(succ_iter):
|
|
def iterate(v):
|
|
for w in succ_iter(v):
|
|
if (v, w) not in ignore_edges:
|
|
yield w
|
|
|
|
return iterate
|
|
|
|
Gpred = filter_pred_iter(Gpred)
|
|
Gsucc = filter_succ_iter(Gsucc)
|
|
|
|
else:
|
|
|
|
def filter_iter(nodes):
|
|
def iterate(v):
|
|
for w in nodes(v):
|
|
if (v, w) not in ignore_edges and (w, v) not in ignore_edges:
|
|
yield w
|
|
|
|
return iterate
|
|
|
|
Gpred = filter_iter(Gpred)
|
|
Gsucc = filter_iter(Gsucc)
|
|
|
|
# predecesssor and successors in search
|
|
pred = {source: None}
|
|
succ = {target: None}
|
|
|
|
# initialize fringes, start with forward
|
|
forward_fringe = [source]
|
|
reverse_fringe = [target]
|
|
|
|
while forward_fringe and reverse_fringe:
|
|
if len(forward_fringe) <= len(reverse_fringe):
|
|
this_level = forward_fringe
|
|
forward_fringe = []
|
|
for v in this_level:
|
|
for w in Gsucc(v):
|
|
if w not in pred:
|
|
forward_fringe.append(w)
|
|
pred[w] = v
|
|
if w in succ:
|
|
# found path
|
|
return pred, succ, w
|
|
else:
|
|
this_level = reverse_fringe
|
|
reverse_fringe = []
|
|
for v in this_level:
|
|
for w in Gpred(v):
|
|
if w not in succ:
|
|
succ[w] = v
|
|
reverse_fringe.append(w)
|
|
if w in pred:
|
|
# found path
|
|
return pred, succ, w
|
|
|
|
raise nx.NetworkXNoPath(f"No path between {source} and {target}.")
|
|
|
|
|
|
def _bidirectional_dijkstra(
|
|
G, source, target, weight="weight", ignore_nodes=None, ignore_edges=None
|
|
):
|
|
"""Dijkstra's algorithm for shortest paths using bidirectional search.
|
|
|
|
This function returns the shortest path between source and target
|
|
ignoring nodes and edges in the containers ignore_nodes and
|
|
ignore_edges.
|
|
|
|
This is a custom modification of the standard Dijkstra bidirectional
|
|
shortest path implementation at networkx.algorithms.weighted
|
|
|
|
Parameters
|
|
----------
|
|
G : NetworkX graph
|
|
|
|
source : node
|
|
Starting node.
|
|
|
|
target : node
|
|
Ending node.
|
|
|
|
weight: string, function, optional (default='weight')
|
|
Edge data key or weight function corresponding to the edge weight
|
|
|
|
ignore_nodes : container of nodes
|
|
nodes to ignore, optional
|
|
|
|
ignore_edges : container of edges
|
|
edges to ignore, optional
|
|
|
|
Returns
|
|
-------
|
|
length : number
|
|
Shortest path length.
|
|
|
|
Returns a tuple of two dictionaries keyed by node.
|
|
The first dictionary stores distance from the source.
|
|
The second stores the path from the source to that node.
|
|
|
|
Raises
|
|
------
|
|
NetworkXNoPath
|
|
If no path exists between source and target.
|
|
|
|
Notes
|
|
-----
|
|
Edge weight attributes must be numerical.
|
|
Distances are calculated as sums of weighted edges traversed.
|
|
|
|
In practice bidirectional Dijkstra is much more than twice as fast as
|
|
ordinary Dijkstra.
|
|
|
|
Ordinary Dijkstra expands nodes in a sphere-like manner from the
|
|
source. The radius of this sphere will eventually be the length
|
|
of the shortest path. Bidirectional Dijkstra will expand nodes
|
|
from both the source and the target, making two spheres of half
|
|
this radius. Volume of the first sphere is pi*r*r while the
|
|
others are 2*pi*r/2*r/2, making up half the volume.
|
|
|
|
This algorithm is not guaranteed to work if edge weights
|
|
are negative or are floating point numbers
|
|
(overflows and roundoff errors can cause problems).
|
|
|
|
See Also
|
|
--------
|
|
shortest_path
|
|
shortest_path_length
|
|
"""
|
|
if ignore_nodes and (source in ignore_nodes or target in ignore_nodes):
|
|
raise nx.NetworkXNoPath(f"No path between {source} and {target}.")
|
|
if source == target:
|
|
if source not in G:
|
|
raise nx.NodeNotFound(f"Node {source} not in graph")
|
|
return (0, [source])
|
|
|
|
# handle either directed or undirected
|
|
if G.is_directed():
|
|
Gpred = G.predecessors
|
|
Gsucc = G.successors
|
|
else:
|
|
Gpred = G.neighbors
|
|
Gsucc = G.neighbors
|
|
|
|
# support optional nodes filter
|
|
if ignore_nodes:
|
|
|
|
def filter_iter(nodes):
|
|
def iterate(v):
|
|
for w in nodes(v):
|
|
if w not in ignore_nodes:
|
|
yield w
|
|
|
|
return iterate
|
|
|
|
Gpred = filter_iter(Gpred)
|
|
Gsucc = filter_iter(Gsucc)
|
|
|
|
# support optional edges filter
|
|
if ignore_edges:
|
|
if G.is_directed():
|
|
|
|
def filter_pred_iter(pred_iter):
|
|
def iterate(v):
|
|
for w in pred_iter(v):
|
|
if (w, v) not in ignore_edges:
|
|
yield w
|
|
|
|
return iterate
|
|
|
|
def filter_succ_iter(succ_iter):
|
|
def iterate(v):
|
|
for w in succ_iter(v):
|
|
if (v, w) not in ignore_edges:
|
|
yield w
|
|
|
|
return iterate
|
|
|
|
Gpred = filter_pred_iter(Gpred)
|
|
Gsucc = filter_succ_iter(Gsucc)
|
|
|
|
else:
|
|
|
|
def filter_iter(nodes):
|
|
def iterate(v):
|
|
for w in nodes(v):
|
|
if (v, w) not in ignore_edges and (w, v) not in ignore_edges:
|
|
yield w
|
|
|
|
return iterate
|
|
|
|
Gpred = filter_iter(Gpred)
|
|
Gsucc = filter_iter(Gsucc)
|
|
|
|
push = heappush
|
|
pop = heappop
|
|
# Init: Forward Backward
|
|
dists = [{}, {}] # dictionary of final distances
|
|
paths = [{source: [source]}, {target: [target]}] # dictionary of paths
|
|
fringe = [[], []] # heap of (distance, node) tuples for
|
|
# extracting next node to expand
|
|
seen = [{source: 0}, {target: 0}] # dictionary of distances to
|
|
# nodes seen
|
|
c = count()
|
|
# initialize fringe heap
|
|
push(fringe[0], (0, next(c), source))
|
|
push(fringe[1], (0, next(c), target))
|
|
# neighs for extracting correct neighbor information
|
|
neighs = [Gsucc, Gpred]
|
|
# variables to hold shortest discovered path
|
|
# finaldist = 1e30000
|
|
finalpath = []
|
|
dir = 1
|
|
while fringe[0] and fringe[1]:
|
|
# choose direction
|
|
# dir == 0 is forward direction and dir == 1 is back
|
|
dir = 1 - dir
|
|
# extract closest to expand
|
|
(dist, _, v) = pop(fringe[dir])
|
|
if v in dists[dir]:
|
|
# Shortest path to v has already been found
|
|
continue
|
|
# update distance
|
|
dists[dir][v] = dist # equal to seen[dir][v]
|
|
if v in dists[1 - dir]:
|
|
# if we have scanned v in both directions we are done
|
|
# we have now discovered the shortest path
|
|
return (finaldist, finalpath)
|
|
|
|
wt = _weight_function(G, weight)
|
|
for w in neighs[dir](v):
|
|
if dir == 0: # forward
|
|
minweight = wt(v, w, G.get_edge_data(v, w))
|
|
vwLength = dists[dir][v] + minweight
|
|
else: # back, must remember to change v,w->w,v
|
|
minweight = wt(w, v, G.get_edge_data(w, v))
|
|
vwLength = dists[dir][v] + minweight
|
|
|
|
if w in dists[dir]:
|
|
if vwLength < dists[dir][w]:
|
|
raise ValueError("Contradictory paths found: negative weights?")
|
|
elif w not in seen[dir] or vwLength < seen[dir][w]:
|
|
# relaxing
|
|
seen[dir][w] = vwLength
|
|
push(fringe[dir], (vwLength, next(c), w))
|
|
paths[dir][w] = paths[dir][v] + [w]
|
|
if w in seen[0] and w in seen[1]:
|
|
# see if this path is better than the already
|
|
# discovered shortest path
|
|
totaldist = seen[0][w] + seen[1][w]
|
|
if finalpath == [] or finaldist > totaldist:
|
|
finaldist = totaldist
|
|
revpath = paths[1][w][:]
|
|
revpath.reverse()
|
|
finalpath = paths[0][w] + revpath[1:]
|
|
raise nx.NetworkXNoPath(f"No path between {source} and {target}.")
|