Complex Contagion — Threshold Cascades on Social Networks

Threshold k: 2 Network density: 4 Mode: Complex (k exposures) Simple contagion (k=1) Seed & Spread Reset Network Step

Complex contagion (Centola & Macy 2007): adoption requires k≥2 adopting neighbors — unlike disease spreading (k=1). This creates a fundamental difference: complex contagion cannot bridge weak ties, and cascades get stuck at cluster boundaries. Dense local ties become essential — the opposite of simple contagion where bridges are critical.