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import networkx as nx
__all__ = ["s_metric"]
@nx._dispatchable
def s_metric(G):
"""Returns the s-metric [1]_ of graph.
The s-metric is defined as the sum of the products ``deg(u) * deg(v)``
for every edge ``(u, v)`` in `G`.
Parameters
----------
G : graph
The graph used to compute the s-metric.
Returns
-------
s : float
The s-metric of the graph.
References
----------
.. [1] Lun Li, David Alderson, John C. Doyle, and Walter Willinger,
Towards a Theory of Scale-Free Graphs:
Definition, Properties, and Implications (Extended Version), 2005.
https://arxiv.org/abs/cond-mat/0501169
"""
return float(sum(G.degree(u) * G.degree(v) for (u, v) in G.edges()))
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