# 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