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For K-12 Students · Small-World Network

Small-World Network for a friendship network

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a friendship network live below — adjust the inputs and watch it respond, right in your browser.

Small-World NetworkLive

Watts-Strogatz rewiring

Controls

Presets

Rewiring probability p

Start with an orderly ring where everyone knows their neighbors, then randomly rewire a few connections. Even a handful of long-range shortcuts collapses the average path length — the six-degrees-of-separation effect — while keeping high local clustering. This small-world structure appears in social networks, the brain, and power grids.

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Data Inspector

Rewiring p0.10

Clustering0.000

Avg path length0.00

Governing equation

L \sim \frac{ln N}{ln k} = \frac{ln 24}{ln 4} \approx 0.00, C \approx 0.000, p = 0.10

Reading this result: Small-world regime: a few random shortcuts collapse the average path length while clustering stays high — the six-degrees effect.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Small-World Network for a friendship network" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.