def topological_sort(graph):
"""
Yield the nodes in topological order.
Faster than the networkx version. When fully iterated, raises an exception if the graph contains a cycle.
"""
# Kahn's algorithm
pred = graph.pred
succ = graph.succ
pred_count_mapping = {}
q = []
for node in graph.nodes:
pred_count = len(pred[node])
if pred_count:
pred_count_mapping[node] = pred_count
else:
q.append(node)
while q:
node = q.pop()
for successor in succ[node]:
pred_count_mapping[successor] -= 1
if pred_count_mapping[successor] == 0:
q.append(successor)
yield node
if any(pred_count_mapping.values()):
raise nx.HasACycle("The graph contains a cycle.")
def dag_to_branching(G):
"""Returns a branching representing all (overlapping) paths from
root nodes to leaf nodes in the given directed acyclic graph.
As described in :mod:`networkx.algorithms.tree.recognition`, a
*branching* is a directed forest in which each node has at most one
parent. In other words, a branching is a disjoint union of
*arborescences*. For this function, each node of in-degree zero in
`G` becomes a root of one of the arborescences, and there will be
one leaf node for each distinct path from that root to a leaf node
in `G`.
Each node `v` in `G` with *k* parents becomes *k* distinct nodes in
the returned branching, one for each parent, and the sub-DAG rooted
at `v` is duplicated for each copy. The algorithm then recurses on
the children of each copy of `v`.
Parameters
----------
G : NetworkX graph
A directed acyclic graph.
Returns
-------
DiGraph
The branching in which there is a bijection between root-to-leaf
paths in `G` (in which multiple paths may share the same leaf)
and root-to-leaf paths in the branching (in which there is a
unique path from a root to a leaf).
Each node has an attribute 'source' whose value is the original
node to which this node corresponds. No other graph, node, or
edge attributes are copied into this new graph.
Raises
------
NetworkXNotImplemented
If `G` is not directed, or if `G` is a multigraph.
HasACycle
If `G` is not acyclic.
Examples
--------
To examine which nodes in the returned branching were produced by
which original node in the directed acyclic graph, we can collect
the mapping from source node to new nodes into a dictionary. For
example, consider the directed diamond graph::
>>> from collections import defaultdict
>>> from operator import itemgetter
>>>
>>> G = nx.DiGraph(nx.utils.pairwise("abd"))
>>> G.add_edges_from(nx.utils.pairwise("acd"))
>>> B = nx.dag_to_branching(G)
>>>
>>> sources = defaultdict(set)
>>> for v, source in B.nodes(data="source"):
... sources[source].add(v)
>>> len(sources["a"])
1
>>> len(sources["d"])
2
To copy node attributes from the original graph to the new graph,
you can use a dictionary like the one constructed in the above
example::
>>> for source, nodes in sources.items():
... for v in nodes:
... B.nodes[v].update(G.nodes[source])
Notes
-----
This function is not idempotent in the sense that the node labels in
the returned branching may be uniquely generated each time the
function is invoked. In fact, the node labels may not be integers;
in order to relabel the nodes to be more readable, you can use the
:func:`networkx.convert_node_labels_to_integers` function.
The current implementation of this function uses
:func:`networkx.prefix_tree`, so it is subject to the limitations of
that function.
"""
if has_cycle(G):
msg = "dag_to_branching is only defined for acyclic graphs"
raise nx.HasACycle(msg)
paths = root_to_leaf_paths(G)
B = nx.prefix_tree(paths)
# Remove the synthetic `root`(0) and `NIL`(-1) nodes from the tree
B.remove_node(0)
B.remove_node(-1)
return B
