Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.

[more]
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