Watts Threshold Model — Network Cascades

Each node adopts if fraction of neighbors already adopted exceeds threshold φ. A small seed can trigger a global cascade — or fizzle — depending on the network structure and threshold.

Controls


Nodes adopted:
Adoption %:
Generation: 0
Cascade size:
Watts (2002): cascade condition
depends on vulnerable nodes
(degree k s.t. 1/k < φ → k > 1/φ)

Giant cascade iff: fraction of
vulnerable nodes spans the graph.

φ too high → no cascade
φ too low → no vulnerable nodes
Sweet spot → global cascade

Colors:
Gray = not adopted
Yellow = just adopted
Green = adopted (stable)