"""
=============================
Breadth First Search on Edges
=============================
Algorithms for a breadth-first traversal of edges in a graph.
"""
from collections import deque
import networkx as nx
FORWARD = "forward"
REVERSE = "reverse"
__all__ = ["edge_bfs"]
[docs]def edge_bfs(G, source=None, orientation=None):
"""A directed, breadth-first-search of edges in `G`, beginning at `source`.
Yield the edges of G in a breadth-first-search order continuing until
all edges are generated.
Parameters
----------
G : graph
A directed/undirected graph/multigraph.
source : node, list of nodes
The node from which the traversal begins. If None, then a source
is chosen arbitrarily and repeatedly until all edges from each node in
the graph are searched.
orientation : None | 'original' | 'reverse' | 'ignore' (default: None)
For directed graphs and directed multigraphs, edge traversals need not
respect the original orientation of the edges.
When set to 'reverse' every edge is traversed in the reverse direction.
When set to 'ignore', every edge is treated as undirected.
When set to 'original', every edge is treated as directed.
In all three cases, the yielded edge tuples add a last entry to
indicate the direction in which that edge was traversed.
If orientation is None, the yielded edge has no direction indicated.
The direction is respected, but not reported.
Yields
------
edge : directed edge
A directed edge indicating the path taken by the breadth-first-search.
For graphs, `edge` is of the form `(u, v)` where `u` and `v`
are the tail and head of the edge as determined by the traversal.
For multigraphs, `edge` is of the form `(u, v, key)`, where `key` is
the key of the edge. When the graph is directed, then `u` and `v`
are always in the order of the actual directed edge.
If orientation is not None then the edge tuple is extended to include
the direction of traversal ('forward' or 'reverse') on that edge.
Examples
--------
>>> nodes = [0, 1, 2, 3]
>>> edges = [(0, 1), (1, 0), (1, 0), (2, 0), (2, 1), (3, 1)]
>>> list(nx.edge_bfs(nx.Graph(edges), nodes))
[(0, 1), (0, 2), (1, 2), (1, 3)]
>>> list(nx.edge_bfs(nx.DiGraph(edges), nodes))
[(0, 1), (1, 0), (2, 0), (2, 1), (3, 1)]
>>> list(nx.edge_bfs(nx.MultiGraph(edges), nodes))
[(0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 2, 0), (1, 2, 0), (1, 3, 0)]
>>> list(nx.edge_bfs(nx.MultiDiGraph(edges), nodes))
[(0, 1, 0), (1, 0, 0), (1, 0, 1), (2, 0, 0), (2, 1, 0), (3, 1, 0)]
>>> list(nx.edge_bfs(nx.DiGraph(edges), nodes, orientation="ignore"))
[(0, 1, 'forward'), (1, 0, 'reverse'), (2, 0, 'reverse'), (2, 1, 'reverse'), (3, 1, 'reverse')]
>>> list(nx.edge_bfs(nx.MultiDiGraph(edges), nodes, orientation="ignore"))
[(0, 1, 0, 'forward'), (1, 0, 0, 'reverse'), (1, 0, 1, 'reverse'), (2, 0, 0, 'reverse'), (2, 1, 0, 'reverse'), (3, 1, 0, 'reverse')]
Notes
-----
The goal of this function is to visit edges. It differs from the more
familiar breadth-first-search of nodes, as provided by
:func:`networkx.algorithms.traversal.breadth_first_search.bfs_edges`, in
that it does not stop once every node has been visited. In a directed graph
with edges [(0, 1), (1, 2), (2, 1)], the edge (2, 1) would not be visited
if not for the functionality provided by this function.
The naming of this function is very similar to bfs_edges. The difference
is that 'edge_bfs' yields edges even if they extend back to an already
explored node while 'bfs_edges' 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 report 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.
See Also
--------
bfs_edges
bfs_tree
edge_dfs
"""
nodes = list(G.nbunch_iter(source))
if not nodes:
return
directed = G.is_directed()
kwds = {"data": False}
if G.is_multigraph() is True:
kwds["keys"] = True
# set up edge lookup
if orientation is None:
def edges_from(node):
return iter(G.edges(node, **kwds))
elif not directed or orientation == "original":
def edges_from(node):
for e in G.edges(node, **kwds):
yield e + (FORWARD,)
elif orientation == "reverse":
def edges_from(node):
for e in G.in_edges(node, **kwds):
yield e + (REVERSE,)
elif orientation == "ignore":
def edges_from(node):
for e in G.edges(node, **kwds):
yield e + (FORWARD,)
for e in G.in_edges(node, **kwds):
yield e + (REVERSE,)
else:
raise nx.NetworkXError("invalid orientation argument.")
if directed:
neighbors = G.successors
def edge_id(edge):
# remove direction indicator
return edge[:-1] if orientation is not None else edge
else:
neighbors = G.neighbors
def edge_id(edge):
return (frozenset(edge[:2]),) + edge[2:]
check_reverse = directed and orientation in ("reverse", "ignore")
# start BFS
visited_nodes = {n for n in nodes}
visited_edges = set()
queue = deque([(n, edges_from(n)) for n in nodes])
while queue:
parent, children_edges = queue.popleft()
for edge in children_edges:
if check_reverse and edge[-1] == REVERSE:
child = edge[0]
else:
child = edge[1]
if child not in visited_nodes:
visited_nodes.add(child)
queue.append((child, edges_from(child)))
edgeid = edge_id(edge)
if edgeid not in visited_edges:
visited_edges.add(edgeid)
yield edge