def out_degree_centrality(G):
"""Compute the out-degree centrality for nodes.
The out-degree centrality for a node v is the fraction of nodes its
outgoing edges are connected to.
Parameters
----------
G : graph
A NetworkX graph
Returns
-------
nodes : dictionary
Dictionary of nodes with out-degree centrality as values.
See Also
--------
degree_centrality, in_degree_centrality
Notes
-----
The degree centrality values are normalized by dividing by the maximum
possible degree in a simple graph n-1 where n is the number of nodes in G.
For multigraphs or graphs with self loops the maximum degree might
be higher than n-1 and values of degree centrality greater than 1
are possible.
"""
if not G.is_directed():
raise nx.NetworkXError( \
"out_degree_centrality() not defined for undirected graphs.")
centrality = {}
s = 1.0 / (len(G) - 1.0)
centrality = dict((n, d * s) for n, d in G.out_degree_iter())
return centrality
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