Make a prediction first
Picture a simplified social network: people arranged in a ring, each connected only to their nearest neighbors — plus a few connections randomly rewired to distant strangers instead. How much does just a handful of those random long-range connections change how likely two “strangers” are to share a mutual contact? Try moving the rewiring slider from 0 and watch what happens.
Diagram description: 30 people arranged in a ring, each originally connected to their 2 nearest neighbors on each side. 3 of the 60 connections (shown dashed) have been randomly rewired to a distant person instead of a near neighbor.
Clustering coefficient (how tightly-knit local groups are): 0.414
Average shortest path between two people: 3.46 connections
Chance two "strangers" (not directly connected) share a mutual contact: 20.0%
Click "Run simulation" to see these statistics averaged across many independently rewired networks.
What changed and why
All three statistics and the diagram update live as you change the network size, starting connections, or rewiring fraction — generating and analyzing one network this size is fast enough to do instantly. Run simulation repeats the whole process across many independently rewired networks with the same settings (in a background worker) and reports the average, so you can see whether one diagram’s numbers were typical or a lucky/unlucky draw.
Why a few shortcuts change everything
Starting from a pure ring (0% rewired), reaching someone across the network takes many steps, and clustering is high — your neighbors mostly know each other too. Rewiring even a small fraction of connections to random distant people barely dents that local clustering, but it collapses the average path length between any two people, because a handful of long-range “shortcuts” let information (or an introduction) skip across the whole network almost immediately. This is exactly the mechanism Watts and Strogatz identified: real-world networks can be simultaneously tightly-knit and only a few steps across, because it takes surprisingly few random long-range connections to produce that effect.(Watts & Strogatz, 1998) See networks and small worlds for the full explanation.
Model assumptions
- This is a deliberately simplified toy model: a ring plus random rewiring, not a model of any specific real social network.
- Every node starts with the same number of connections, but after rewiring, individual nodes can end up with more or fewer connections than they started with — only the network-wide average degree is guaranteed to stay fixed. This matches the real Watts-Strogatz rewiring procedure rather than an idealized, degree-preserving version of it.
- Real social ties are not laid out on a simple ring — they cluster by geography, age, profession, and shared institutions in ways this model doesn’t attempt to capture. See independence and dependence for the general point about shared context breaking simple randomness assumptions.
Reproducibility
Every network is seeded: the same size, starting connections, rewiring fraction, and seed always produce the same diagram and statistics. Running the simulation updates this page’s URL so you can share the exact setup.
Sources and method
The rewiring procedure and the closed-form clustering-coefficient formula for an unrewired ring (used to cross-check this tool’s clustering calculation in its unit tests) both follow the original small-world network model.(Watts & Strogatz, 1998) The “chance two strangers share a mutual contact” statistic is this site’s own addition, computed exactly for whichever single network is currently displayed — not estimated — by checking every non-connected pair for a shared neighbor.