"""Functions for generating stochastic graphs from a given weighted directed
from networkx.classes import DiGraph
from networkx.classes import MultiDiGraph
from networkx.utils import not_implemented_for
__all__ = ["stochastic_graph"]
def stochastic_graph(G, copy=True, weight="weight"):
"""Returns a right-stochastic representation of directed graph `G`.
A right-stochastic graph is a weighted digraph in which for each
node, the sum of the weights of all the out-edges of that node is
1. If the graph is already weighted (for example, via a 'weight'
edge attribute), the reweighting takes that into account.
G : directed graph
A :class:`~networkx.DiGraph` or :class:`~networkx.MultiDiGraph`.
copy : boolean, optional
If this is True, then this function returns a new graph with
the stochastic reweighting. Otherwise, the original graph is
modified in-place (and also returned, for convenience).
weight : edge attribute key (optional, default='weight')
Edge attribute key used for reading the existing weight and
setting the new weight. If no attribute with this key is found
for an edge, then the edge weight is assumed to be 1. If an edge
has a weight, it must be a positive number.
G = MultiDiGraph(G) if G.is_multigraph() else DiGraph(G)
# There is a tradeoff here: the dictionary of node degrees may
# require a lot of memory, whereas making a call to `G.out_degree`
# inside the loop may be costly in computation time.
degree = dict(G.out_degree(weight=weight))
for u, v, d in G.edges(data=True):
if degree[u] == 0:
d[weight] = 0
d[weight] = d.get(weight, 1) / degree[u]