Home▸Networks & Graph Theory▸Erdos-Renyi Percolation Simulator

🕸️ Erdős–Rényi Percolation

Interactive 3D random graph where adjusting edge-connection probability shows the network suddenly transitioning from scattered fragments to one giant connected component at the percolation threshold.

Networks & Graph Theory3DModerate60 FPS

A 3D random graph of N nodes where every possible edge is drawn independently with probability p, letting you watch the network snap from scattered fragments into one dominant giant component as the average degree crosses 1.

🔬 What It Demonstrates

Erdős–Rényi random graphs undergo a sharp phase transition at average degree ⟨c⟩ = 1: below it, components stay small and numerous; above it, a single component absorbs a finite fraction of all nodes almost overnight.

🎮 How to Use

Set the node count and drag the average-degree slider slowly through ⟨c⟩ = 1 while watching the highlighted giant component and live component statistics. Reroll to see a fresh random draw at the same settings.

💡 Did You Know?

The same ⟨c⟩ = 1 threshold governs epidemic outbreak size (basic reproduction number R₀), lattice bond percolation, and the robustness of real communication networks to random failures.

⚙ Under the hood

Interactive 3D random graph where dialing edge probability shows how a giant connected component suddenly emerges at the Erdos-Renyi percolation threshold.

erdos-renyipercolationrandom-graphsphase-transitionsgraph-theorynetworks

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install