def find_cycle(G, source=None, orientation='original'):
"""
Returns the edges of a cycle found via a directed, depth-first traversal.
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 : 'original' | 'reverse' | 'ignore'
For directed graphs and directed multigraphs, edge traversals need not
respect the original orientation of the edges. When set to 'reverse',
then every edge will be traversed in the reverse direction. When set to
'ignore', then each directed edge is treated as a single undirected
edge that can be traversed in either direction. For undirected graphs
and undirected multigraphs, this parameter is meaningless and is not
consulted by the algorithm.
Returns
-------
edges : directed edges
A list of directed edges indicating the path taken for the loop. If
no cycle is found, then ``edges`` will be an empty list. For graphs, an
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, an 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 'ignore', then an edge takes
the form (u, v, key, direction) where direction indicates if the edge
was followed in the forward (tail to head) or reverse (head to tail)
direction. When the direction is forward, the value of ``direction``
is 'forward'. When the direction is reverse, the value of ``direction``
is 'reverse'.
Examples
--------
In this example, we construct a DAG and find, in the first call, that there
are no directed cycles, and so an exception is raised. In the second call,
we ignore edge orientations and find that there is an undirected cycle.
Note that the second call finds a directed cycle while effectively
traversing an undirected graph, and so, we found an "undirected cycle".
This means that this DAG structure does not form a directed tree (which
is also known as a polytree).
>>> import networkx as nx
>>> G = nx.DiGraph([(0,1), (0,2), (1,2)])
>>> try:
... find_cycle(G, orientation='original')
... except:
... pass
...
>>> list(find_cycle(G, orientation='ignore'))
[(0, 1, 'forward'), (1, 2, 'forward'), (0, 2, 'reverse')]
"""
out_edge, key, tailhead = helper_funcs(G, orientation)
explored = set()
cycle = []
final_node = None
for start_node in G.nbunch_iter(source):
if start_node in explored:
# No loop is possible.
continue
edges = []
# All nodes seen in this iteration of edge_dfs
seen = {start_node}
# Nodes in active path.
active_nodes = {start_node}
previous_node = None
for edge in edge_dfs(G, start_node, orientation):
# Determine if this edge is a continuation of the active path.
tail, head = tailhead(edge)
if previous_node is not None and tail != previous_node:
# This edge results from backtracking.
# Pop until we get a node whose head equals the current tail.
# So for example, we might have:
# (0,1), (1,2), (2,3), (1,4)
# which must become:
# (0,1), (1,4)
while True:
try:
popped_edge = edges.pop()
except IndexError:
edges = []
active_nodes = {tail}
break
else:
popped_head = tailhead(popped_edge)[1]
active_nodes.remove(popped_head)
if edges:
last_head = tailhead(edges[-1])[1]
if tail == last_head:
break
edges.append(edge)
if head in active_nodes:
# We have a loop!
cycle.extend(edges)
final_node = head
break
elif head in explored:
# Then we've already explored it. No loop is possible.
break
else:
seen.add(head)
active_nodes.add(head)
previous_node = head
if cycle:
break
else:
explored.update(seen)
else:
assert(len(cycle) == 0)
raise nx.exception.NetworkXNoCycle('No cycle found.')
# We now have a list of edges which ends on a cycle.
# So we need to remove from the beginning edges that are not relevant.
for i, edge in enumerate(cycle):
tail, head = tailhead(edge)
if tail == final_node:
break
return cycle[i:]
def find_cycle(G, source=None):
orientation='original'
out_edge, key, tailhead = helper_funcs(G, orientation)
explored = set()
cycle = []
final_node = None
for start_node in G.nbunch_iter(source):
if start_node in explored:
# No loop is possible.
continue
edges = []
# All nodes seen in this iteration of edge_dfs
seen = {start_node}
# Nodes in active path.
active_nodes = {start_node}
previous_node = None
for edge in edge_dfs(G, start_node, orientation):
# Determine if this edge is a continuation of the active path.
tail, head = tailhead(edge)
if previous_node is not None and tail != previous_node:
""" This edge results from backtracking.
Pop until we get a node whose head equals the current tail.
So for example, we might have:
(0,1), (1,2), (2,3), (1,4)
which must become:
(0,1), (1,4)
"""
while True:
try:
popped_edge = edges.pop()
except IndexError:
edges = []
active_nodes = {tail}
break
else:
popped_head = tailhead(popped_edge)[1]
active_nodes.remove(popped_head)
if edges:
last_head = tailhead(edges[-1])[1]
if tail == last_head:
break
edges.append(edge)
if head in active_nodes:
# We have a loop!
cycle.extend(edges)
final_node = head
break
elif head in explored:
# Then we've already explored it. No loop is possible.
break
else:
seen.add(head)
active_nodes.add(head)
previous_node = head
if cycle:
break
else:
explored.update(seen)
else:
assert(len(cycle) == 0)
raise nx.exception.NetworkXNoCycle('No cycle found.')
# We now have a list of edges which ends on a cycle.
# So we need to remove from the beginning edges that are not relevant.
for i, edge in enumerate(cycle):
tail, head = tailhead(edge)
if tail == final_node:
break
return cycle[i:]
def find_cycle(G, source=None, orientation='original'):
out_edge, key, tailhead = helper_funcs(G, orientation)
explored = set()
cycle = []
final_node = None
for start_node in G.nbunch_iter(source):
if start_node in explored:
# No loop is possible.
continue
edges = []
# All nodes seen in this iteration of edge_dfs
seen = {start_node}
# Nodes in active path.
active_nodes = {start_node}
previous_node = None
for edge in edge_dfs(G, start_node, orientation):
# Determine if this edge is a continuation of the active path.
tail, head = tailhead(edge)
if previous_node is not None and tail != previous_node:
# This edge results from backtracking.
# Pop until we get a node whose head equals the current tail.
# So for example, we might have:
# (0,1), (1,2), (2,3), (1,4)
# which must become:
# (0,1), (1,4)
while True:
try:
popped_edge = edges.pop()
except IndexError:
edges = []
active_nodes = {tail}
break
else:
popped_head = tailhead(popped_edge)[1]
active_nodes.remove(popped_head)
if edges:
last_head = tailhead(edges[-1])[1]
if tail == last_head:
break
edges.append(edge)
if head in active_nodes:
# We have a loop!
cycle.extend(edges)
final_node = head
break
elif head in explored:
# Then we've already explored it. No loop is possible.
break
else:
seen.add(head)
active_nodes.add(head)
previous_node = head
if cycle:
break
else:
explored.update(seen)
else:
assert(len(cycle) == 0)
raise nx.exception.NetworkXNoCycle('No cycle found.')
# We now have a list of edges which ends on a cycle.
# So we need to remove from the beginning edges that are not relevant.
for i, edge in enumerate(cycle):
tail, head = tailhead(edge)
if tail == final_node:
break
return cycle
def find_cycle(G, source=None, orientation='original'):
"""
Returns the edges of a cycle found via a directed, depth-first traversal.
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 : 'original' | 'reverse' | 'ignore'
For directed graphs and directed multigraphs, edge traversals need not
respect the original orientation of the edges. When set to 'reverse',
then every edge will be traversed in the reverse direction. When set to
'ignore', then each directed edge is treated as a single undirected
edge that can be traversed in either direction. For undirected graphs
and undirected multigraphs, this parameter is meaningless and is not
consulted by the algorithm.
Returns
-------
edges : directed edges
A list of directed edges indicating the path taken for the loop. If
no cycle is found, then ``edges`` will be an empty list. For graphs, an
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, an 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 'ignore', then an edge takes
the form (u, v, key, direction) where direction indicates if the edge
was followed in the forward (tail to head) or reverse (head to tail)
direction. When the direction is forward, the value of ``direction``
is 'forward'. When the direction is reverse, the value of ``direction``
is 'reverse'.
Examples
--------
In this example, we construct a DAG and find, in the first call, that there
are no directed cycles, and so an exception is raised. In the second call,
we ignore edge orientations and find that there is an undirected cycle.
Note that the second call finds a directed cycle while effectively
traversing an undirected graph, and so, we found an "undirected cycle".
This means that this DAG structure does not form a directed tree (which
is also known as a polytree).
>>> import networkx as nx
>>> G = nx.DiGraph([(0,1), (0,2), (1,2)])
>>> try:
... find_cycle(G, orientation='original')
... except:
... pass
...
>>> list(find_cycle(G, orientation='ignore'))
[(0, 1, 'forward'), (1, 2, 'forward'), (0, 2, 'reverse')]
"""
out_edge, key, tailhead = helper_funcs(G, orientation)
explored = set()
cycle = []
final_node = None
for start_node in G.nbunch_iter(source):
if start_node in explored:
# No loop is possible.
continue
edges = []
# All nodes seen in this iteration of edge_dfs
seen = {start_node}
# Nodes in active path.
active_nodes = {start_node}
previous_node = None
for edge in edge_dfs(G, start_node, orientation):
# Determine if this edge is a continuation of the active path.
tail, head = tailhead(edge)
if previous_node is not None and tail != previous_node:
# This edge results from backtracking.
# Pop until we get a node whose head equals the current tail.
# So for example, we might have:
# (0,1), (1,2), (2,3), (1,4)
# which must become:
# (0,1), (1,4)
while True:
try:
popped_edge = edges.pop()
except IndexError:
edges = []
active_nodes = {tail}
break
else:
popped_head = tailhead(popped_edge)[1]
active_nodes.remove(popped_head)
if edges:
last_head = tailhead(edges[-1])[1]
if tail == last_head:
break
edges.append(edge)
if head in active_nodes:
# We have a loop!
cycle.extend(edges)
final_node = head
break
elif head in explored:
# Then we've already explored it. No loop is possible.
break
else:
seen.add(head)
active_nodes.add(head)
previous_node = head
if cycle:
break
else:
explored.update(seen)
else:
assert (len(cycle) == 0)
raise nx.exception.NetworkXNoCycle('No cycle found.')
# We now have a list of edges which ends on a cycle.
# So we need to remove from the beginning edges that are not relevant.
for i, edge in enumerate(cycle):
tail, head = tailhead(edge)
if tail == final_node:
break
return cycle[i:]