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import networkx as nx
__all__ = ["s_metric"]
@nx.dispatch
def s_metric(G, normalized=True):
"""Returns the s-metric of graph.
The s-metric is defined as the sum of the products deg(u)*deg(v)
for every edge (u,v) in G. If norm is provided construct the
s-max graph and compute it's s_metric, and return the normalized
s value
Parameters
----------
G : graph
The graph used to compute the s-metric.
normalized : bool (optional)
Normalize the value.
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
"""
if normalized:
raise nx.NetworkXError("Normalization not implemented")
# Gmax = li_smax_graph(list(G.degree().values()))
# return s_metric(G,normalized=False)/s_metric(Gmax,normalized=False)
# else:
return float(sum(G.degree(u) * G.degree(v) for (u, v) in G.edges()))
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