Random Matrix Theory Applied to Small-World Networks

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This Demonstration shows an application of random matrix theory to complex networks, in particular, small-world network realizations according to the Watts–Strogatz model implemented in the Wolfram Language function WattsStrogatzGraphDistribution.
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Contributed by: Jessica Alfonsi (December 2020)
(Padova, Italy)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: Poisson distribution in the (almost) regular graph regime, very small rewiring probability
Snapshot 2: network graph corresponding to Snapshot 1
Snapshot 3: critical distribution at the onset of small-world regime (), rewiring probability
Snapshot 4: network graph corresponding to Snapshot 3
Snapshot 5: Wigner distribution in random graph regime, rewiring probability
Snapshot 6: network graph corresponding to Snapshot 5
Reference
[1] J. N. Bandyopadhyay and S. Jalan, "Universality in Complex Networks: Random Matrix Analysis," Physical Review E, 76(2), 2007 026109. doi:10.1103/PhysRevE.76.026109.
Permanent Citation