Bootstrap Percolation & k-Core Pruning

Bootstrap percolation removes nodes with fewer than k active neighbors iteratively. This process can exhibit a discontinuous (first-order) transition: below a threshold, only a small fraction survives; above it, a macroscopic core persists. This models contagion, financial cascades, and network robustness.

Network size N: 80

Mean degree ⟨k⟩: 4.0

Bootstrap threshold m: 2

Initial seed fraction: 0.5

Generate a network to begin

k-core: maximal subgraph where every node has degree ≥ k

Discontinuous transition: at critical seed density ρ_c, surviving fraction jumps from ~0 to S > 0

Node colors: orange=active, gray=pruned, white=seed