"""
===========================
Depth First Search on Edges
===========================
Algorithms for a depth-first traversal of edges in a graph.
"""
import networkx as nx
FORWARD = "forward"
REVERSE = "reverse"
__all__ = ["edge_dfs"]
[docs]def edge_dfs(G, source=None, orientation=None):
"""A directed, depth-first-search of edges in `G`, beginning at `source`.
Yield the edges of G in a depth-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 depth-first traversal.
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, 1), (3, 1)]
>>> list(nx.edge_dfs(nx.Graph(edges), nodes))
[(0, 1), (1, 2), (1, 3)]
>>> list(nx.edge_dfs(nx.DiGraph(edges), nodes))
[(0, 1), (1, 0), (2, 1), (3, 1)]
>>> list(nx.edge_dfs(nx.MultiGraph(edges), nodes))
[(0, 1, 0), (1, 0, 1), (0, 1, 2), (1, 2, 0), (1, 3, 0)]
>>> list(nx.edge_dfs(nx.MultiDiGraph(edges), nodes))
[(0, 1, 0), (1, 0, 0), (1, 0, 1), (2, 1, 0), (3, 1, 0)]
>>> list(nx.edge_dfs(nx.DiGraph(edges), nodes, orientation="ignore"))
[(0, 1, 'forward'), (1, 0, 'forward'), (2, 1, 'reverse'), (3, 1, 'reverse')]
>>> list(nx.edge_dfs(nx.MultiDiGraph(edges), nodes, orientation="ignore"))
[(0, 1, 0, 'forward'), (1, 0, 0, 'forward'), (1, 0, 1, '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 depth-first traversal of nodes, as provided by
:func:`networkx.algorithms.traversal.depth_first_search.dfs_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.
See Also
--------
dfs_edges
"""
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.")
# set up formation of edge_id to easily look up if edge already returned
if directed:
def edge_id(edge):
# remove direction indicator
return edge[:-1] if orientation is not None else edge
else:
def edge_id(edge):
# single id for undirected requires frozenset on nodes
return (frozenset(edge[:2]),) + edge[2:]
# Basic setup
check_reverse = directed and orientation in ("reverse", "ignore")
visited_edges = set()
visited_nodes = set()
edges = {}
# start DFS
for start_node in nodes:
stack = [start_node]
while stack:
current_node = stack[-1]
if current_node not in visited_nodes:
edges[current_node] = edges_from(current_node)
visited_nodes.add(current_node)
try:
edge = next(edges[current_node])
except StopIteration:
# No more edges from the current node.
stack.pop()
else:
edgeid = edge_id(edge)
if edgeid not in visited_edges:
visited_edges.add(edgeid)
# Mark the traversed "to" node as to-be-explored.
if check_reverse and edge[-1] == REVERSE:
stack.append(edge[0])
else:
stack.append(edge[1])
yield edge