90 lines
3.4 KiB
Python
90 lines
3.4 KiB
Python
"""Basic algorithms for breadth-first searching the nodes of a graph."""
|
|
|
|
import networkx as nx
|
|
|
|
__all__ = ["bfs_beam_edges"]
|
|
|
|
|
|
@nx._dispatchable
|
|
def bfs_beam_edges(G, source, value, width=None):
|
|
"""Iterates over edges in a beam search.
|
|
|
|
The beam search is a generalized breadth-first search in which only
|
|
the "best" *w* neighbors of the current node are enqueued, where *w*
|
|
is the beam width and "best" is an application-specific
|
|
heuristic. In general, a beam search with a small beam width might
|
|
not visit each node in the graph.
|
|
|
|
.. note::
|
|
|
|
With the default value of ``width=None`` or `width` greater than the
|
|
maximum degree of the graph, this function equates to a slower
|
|
version of `~networkx.algorithms.traversal.breadth_first_search.bfs_edges`.
|
|
All nodes will be visited, though the order of the reported edges may
|
|
vary. In such cases, `value` has no effect - consider using `bfs_edges`
|
|
directly instead.
|
|
|
|
Parameters
|
|
----------
|
|
G : NetworkX graph
|
|
|
|
source : node
|
|
Starting node for the breadth-first search; this function
|
|
iterates over only those edges in the component reachable from
|
|
this node.
|
|
|
|
value : function
|
|
A function that takes a node of the graph as input and returns a
|
|
real number indicating how "good" it is. A higher value means it
|
|
is more likely to be visited sooner during the search. When
|
|
visiting a new node, only the `width` neighbors with the highest
|
|
`value` are enqueued (in decreasing order of `value`).
|
|
|
|
width : int (default = None)
|
|
The beam width for the search. This is the number of neighbors
|
|
(ordered by `value`) to enqueue when visiting each new node.
|
|
|
|
Yields
|
|
------
|
|
edge
|
|
Edges in the beam search starting from `source`, given as a pair
|
|
of nodes.
|
|
|
|
Examples
|
|
--------
|
|
To give nodes with, for example, a higher centrality precedence
|
|
during the search, set the `value` function to return the centrality
|
|
value of the node:
|
|
|
|
>>> G = nx.karate_club_graph()
|
|
>>> centrality = nx.eigenvector_centrality(G)
|
|
>>> list(nx.bfs_beam_edges(G, source=0, value=centrality.get, width=3))
|
|
[(0, 2), (0, 1), (0, 8), (2, 32), (1, 13), (8, 33)]
|
|
"""
|
|
|
|
if width is None:
|
|
width = len(G)
|
|
|
|
def successors(v):
|
|
"""Returns a list of the best neighbors of a node.
|
|
|
|
`v` is a node in the graph `G`.
|
|
|
|
The "best" neighbors are chosen according to the `value`
|
|
function (higher is better). Only the `width` best neighbors of
|
|
`v` are returned.
|
|
"""
|
|
# TODO The Python documentation states that for small values, it
|
|
# is better to use `heapq.nlargest`. We should determine the
|
|
# threshold at which its better to use `heapq.nlargest()`
|
|
# instead of `sorted()[:]` and apply that optimization here.
|
|
#
|
|
# If `width` is greater than the number of neighbors of `v`, all
|
|
# neighbors are returned by the semantics of slicing in
|
|
# Python. This occurs in the special case that the user did not
|
|
# specify a `width`: in this case all neighbors are always
|
|
# returned, so this is just a (slower) implementation of
|
|
# `bfs_edges(G, source)` but with a sorted enqueue step.
|
|
return iter(sorted(G.neighbors(v), key=value, reverse=True)[:width])
|
|
|
|
yield from nx.generic_bfs_edges(G, source, successors)
|