"""Basic algorithms for breadth-first searching the nodes of a graph."""
import networkx as nx
from collections import deque
__all__ = [
"bfs_edges",
"bfs_tree",
"bfs_predecessors",
"bfs_successors",
"descendants_at_distance",
]
def generic_bfs_edges(G, source, neighbors=None, depth_limit=None, sort_neighbors=None):
"""Iterate over edges in a breadth-first search.
The breadth-first search begins at `source` and enqueues the
neighbors of newly visited nodes specified by the `neighbors`
function.
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.
neighbors : function
A function that takes a newly visited node of the graph as input
and returns an *iterator* (not just a list) of nodes that are
neighbors of that node. If not specified, this is just the
``G.neighbors`` method, but in general it can be any function
that returns an iterator over some or all of the neighbors of a
given node, in any order.
depth_limit : int, optional(default=len(G))
Specify the maximum search depth
sort_neighbors : function
A function that takes the list of neighbors of given node as input, and
returns an *iterator* over these neighbors but with custom ordering.
Yields
------
edge
Edges in the breadth-first search starting from `source`.
Examples
--------
>>> G = nx.path_graph(3)
>>> print(list(nx.bfs_edges(G, 0)))
[(0, 1), (1, 2)]
>>> print(list(nx.bfs_edges(G, source=0, depth_limit=1)))
[(0, 1)]
Notes
-----
This implementation is from `PADS`_, which was in the public domain
when it was first accessed in July, 2004. The modifications
to allow depth limits are based on the Wikipedia article
"`Depth-limited-search`_".
.. _PADS: http://www.ics.uci.edu/~eppstein/PADS/BFS.py
.. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search
"""
if callable(sort_neighbors):
_neighbors = neighbors
neighbors = lambda node: iter(sort_neighbors(_neighbors(node)))
visited = {source}
if depth_limit is None:
depth_limit = len(G)
queue = deque([(source, depth_limit, neighbors(source))])
while queue:
parent, depth_now, children = queue[0]
try:
child = next(children)
if child not in visited:
yield parent, child
visited.add(child)
if depth_now > 1:
queue.append((child, depth_now - 1, neighbors(child)))
except StopIteration:
queue.popleft()
[文档]def bfs_edges(G, source, reverse=False, depth_limit=None, sort_neighbors=None):
"""Iterate over edges in a breadth-first-search starting at source.
Parameters
----------
G : NetworkX graph
source : node
Specify starting node for breadth-first search; this function
iterates over only those edges in the component reachable from
this node.
reverse : bool, optional
If True traverse a directed graph in the reverse direction
depth_limit : int, optional(default=len(G))
Specify the maximum search depth
sort_neighbors : function
A function that takes the list of neighbors of given node as input, and
returns an *iterator* over these neighbors but with custom ordering.
Yields
------
edge: 2-tuple of nodes
Yields edges resulting from the breadth-first search.
Examples
--------
To get the edges in a breadth-first search::
>>> G = nx.path_graph(3)
>>> list(nx.bfs_edges(G, 0))
[(0, 1), (1, 2)]
>>> list(nx.bfs_edges(G, source=0, depth_limit=1))
[(0, 1)]
To get the nodes in a breadth-first search order::
>>> G = nx.path_graph(3)
>>> root = 2
>>> edges = nx.bfs_edges(G, root)
>>> nodes = [root] + [v for u, v in edges]
>>> nodes
[2, 1, 0]
Notes
-----
The naming of this function is very similar to
:func:`~networkx.algorithms.traversal.edgebfs.edge_bfs`. The difference
is that ``edge_bfs`` yields edges even if they extend back to an already
explored node while this generator yields the edges of the tree that results
from a breadth-first-search (BFS) so no edges are reported if they extend
to already explored nodes. That means ``edge_bfs`` reports all edges while
``bfs_edges`` only reports those traversed by a node-based BFS. Yet another
description is that ``bfs_edges`` reports the edges traversed during BFS
while ``edge_bfs`` reports all edges in the order they are explored.
Based on the breadth-first search implementation in PADS [1]_
by D. Eppstein, July 2004; with modifications to allow depth limits
as described in [2]_.
References
----------
.. [1] http://www.ics.uci.edu/~eppstein/PADS/BFS.py.
.. [2] https://en.wikipedia.org/wiki/Depth-limited_search
See Also
--------
bfs_tree
:func:`~networkx.algorithms.traversal.depth_first_search.dfs_edges`
:func:`~networkx.algorithms.traversal.edgebfs.edge_bfs`
"""
if reverse and G.is_directed():
successors = G.predecessors
else:
successors = G.neighbors
yield from generic_bfs_edges(G, source, successors, depth_limit, sort_neighbors)
[文档]def bfs_tree(G, source, reverse=False, depth_limit=None, sort_neighbors=None):
"""Returns an oriented tree constructed from of a breadth-first-search
starting at source.
Parameters
----------
G : NetworkX graph
source : node
Specify starting node for breadth-first search
reverse : bool, optional
If True traverse a directed graph in the reverse direction
depth_limit : int, optional(default=len(G))
Specify the maximum search depth
sort_neighbors : function
A function that takes the list of neighbors of given node as input, and
returns an *iterator* over these neighbors but with custom ordering.
Returns
-------
T: NetworkX DiGraph
An oriented tree
Examples
--------
>>> G = nx.path_graph(3)
>>> print(list(nx.bfs_tree(G, 1).edges()))
[(1, 0), (1, 2)]
>>> H = nx.Graph()
>>> nx.add_path(H, [0, 1, 2, 3, 4, 5, 6])
>>> nx.add_path(H, [2, 7, 8, 9, 10])
>>> print(sorted(list(nx.bfs_tree(H, source=3, depth_limit=3).edges())))
[(1, 0), (2, 1), (2, 7), (3, 2), (3, 4), (4, 5), (5, 6), (7, 8)]
Notes
-----
Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py
by D. Eppstein, July 2004. The modifications
to allow depth limits based on the Wikipedia article
"`Depth-limited-search`_".
.. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search
See Also
--------
dfs_tree
bfs_edges
edge_bfs
"""
T = nx.DiGraph()
T.add_node(source)
edges_gen = bfs_edges(
G,
source,
reverse=reverse,
depth_limit=depth_limit,
sort_neighbors=sort_neighbors,
)
T.add_edges_from(edges_gen)
return T
[文档]def bfs_predecessors(G, source, depth_limit=None, sort_neighbors=None):
"""Returns an iterator of predecessors in breadth-first-search from source.
Parameters
----------
G : NetworkX graph
source : node
Specify starting node for breadth-first search
depth_limit : int, optional(default=len(G))
Specify the maximum search depth
sort_neighbors : function
A function that takes the list of neighbors of given node as input, and
returns an *iterator* over these neighbors but with custom ordering.
Returns
-------
pred: iterator
(node, predecessor) iterator where `predecessor` is the predecessor of
`node` in a breadth first search starting from `source`.
Examples
--------
>>> G = nx.path_graph(3)
>>> print(dict(nx.bfs_predecessors(G, 0)))
{1: 0, 2: 1}
>>> H = nx.Graph()
>>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)])
>>> print(dict(nx.bfs_predecessors(H, 0)))
{1: 0, 2: 0, 3: 1, 4: 1, 5: 2, 6: 2}
>>> M = nx.Graph()
>>> nx.add_path(M, [0, 1, 2, 3, 4, 5, 6])
>>> nx.add_path(M, [2, 7, 8, 9, 10])
>>> print(sorted(nx.bfs_predecessors(M, source=1, depth_limit=3)))
[(0, 1), (2, 1), (3, 2), (4, 3), (7, 2), (8, 7)]
>>> N = nx.DiGraph()
>>> nx.add_path(N, [0, 1, 2, 3, 4, 7])
>>> nx.add_path(N, [3, 5, 6, 7])
>>> print(sorted(nx.bfs_predecessors(N, source=2)))
[(3, 2), (4, 3), (5, 3), (6, 5), (7, 4)]
Notes
-----
Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py
by D. Eppstein, July 2004. The modifications
to allow depth limits based on the Wikipedia article
"`Depth-limited-search`_".
.. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search
See Also
--------
bfs_tree
bfs_edges
edge_bfs
"""
for s, t in bfs_edges(
G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors
):
yield (t, s)
[文档]def bfs_successors(G, source, depth_limit=None, sort_neighbors=None):
"""Returns an iterator of successors in breadth-first-search from source.
Parameters
----------
G : NetworkX graph
source : node
Specify starting node for breadth-first search
depth_limit : int, optional(default=len(G))
Specify the maximum search depth
sort_neighbors : function
A function that takes the list of neighbors of given node as input, and
returns an *iterator* over these neighbors but with custom ordering.
Returns
-------
succ: iterator
(node, successors) iterator where `successors` is the non-empty list of
successors of `node` in a breadth first search from `source`.
To appear in the iterator, `node` must have successors.
Examples
--------
>>> G = nx.path_graph(3)
>>> print(dict(nx.bfs_successors(G, 0)))
{0: [1], 1: [2]}
>>> H = nx.Graph()
>>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)])
>>> print(dict(nx.bfs_successors(H, 0)))
{0: [1, 2], 1: [3, 4], 2: [5, 6]}
>>> G = nx.Graph()
>>> nx.add_path(G, [0, 1, 2, 3, 4, 5, 6])
>>> nx.add_path(G, [2, 7, 8, 9, 10])
>>> print(dict(nx.bfs_successors(G, source=1, depth_limit=3)))
{1: [0, 2], 2: [3, 7], 3: [4], 7: [8]}
>>> G = nx.DiGraph()
>>> nx.add_path(G, [0, 1, 2, 3, 4, 5])
>>> print(dict(nx.bfs_successors(G, source=3)))
{3: [4], 4: [5]}
Notes
-----
Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py
by D. Eppstein, July 2004.The modifications
to allow depth limits based on the Wikipedia article
"`Depth-limited-search`_".
.. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search
See Also
--------
bfs_tree
bfs_edges
edge_bfs
"""
parent = source
children = []
for p, c in bfs_edges(
G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors
):
if p == parent:
children.append(c)
continue
yield (parent, children)
children = [c]
parent = p
yield (parent, children)
[文档]def descendants_at_distance(G, source, distance):
"""Returns all nodes at a fixed `distance` from `source` in `G`.
Parameters
----------
G : NetworkX graph
A graph
source : node in `G`
distance : the distance of the wanted nodes from `source`
Returns
-------
set()
The descendants of `source` in `G` at the given `distance` from `source`
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.descendants_at_distance(G, 2, 2)
{0, 4}
>>> H = nx.DiGraph()
>>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)])
>>> nx.descendants_at_distance(H, 0, 2)
{3, 4, 5, 6}
>>> nx.descendants_at_distance(H, 5, 0)
{5}
>>> nx.descendants_at_distance(H, 5, 1)
set()
"""
if not G.has_node(source):
raise nx.NetworkXError(f"The node {source} is not in the graph.")
current_distance = 0
current_layer = {source}
visited = {source}
# this is basically BFS, except that the current layer only stores the nodes at
# current_distance from source at each iteration
while current_distance < distance:
next_layer = set()
for node in current_layer:
for child in G[node]:
if child not in visited:
visited.add(child)
next_layer.add(child)
current_layer = next_layer
current_distance += 1
return current_layer