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networkx.algorithms.smallworld.sigma

sigma(G, niter=100, nrand=10, seed=None)

Returns the small-world coefficient (sigma) of the given graph.

The small-world coefficient is defined as: sigma = C/Cr / L/Lr where C and L are respectively the average clustering coefficient and average shortest path length of G. Cr and Lr are respectively the average clustering coefficient and average shortest path length of an equivalent random graph.

A graph is commonly classified as small-world if sigma>1.

Parameters

• G (NetworkX graph) – An undirected graph.

• niter (integer (optional, default=100)) – Approximate number of rewiring per edge to compute the equivalent random graph.

• nrand (integer (optional, default=10)) – Number of random graphs generated to compute the average clustering coefficient (Cr) and average shortest path length (Lr).

• seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.

Returns

sigma – The small-world coefficient of G.

Return type

float

Notes

The implementation is adapted from Humphries et al. 1 2.

References

1

The brainstem reticular formation is a small-world, not scale-free, network M. D. Humphries, K. Gurney and T. J. Prescott, Proc. Roy. Soc. B 2006 273, 503-511, doi:10.1098/rspb.2005.3354.

2

Humphries and Gurney (2008). “Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence”. PLoS One. 3 (4). PMID 18446219. doi:10.1371/journal.pone.0002051.