Each of the 56 nodes is an organisation — a quantum-hardware startup, a university lab, a national metrology institute — and each edge is a bilateral partnership. This is Watts' linear threshold model for cascades on a network (Watts, 2002): every node i has a random adoption threshold θᵢ, and it switches from "not adopted" to "adopted" once the fraction of its already-adopted partners reaches that threshold:
node i adopts when: (adopted neighbors of i) / (degree of i) ≥ θᵢ
Update rule (synchronous): all nodes are re-evaluated each tick t → t+1
using the adoption state at tick t, so a cascade unfolds one hop per step.
A handful of seed adopters (gold) start already-committed — think of them as the first consortium to sign a joint-development agreement. Whether their commitment spreads to the whole network or fizzles out after one or two hops depends on two knobs:
- Partnership density — the average number of ties per node. Below a critical average degree the network is too sparse to carry a cascade past its immediate neighbours; above it, a single seed can percolate through the whole graph. This is the same connectivity threshold that governs giant-component formation in random graphs.
- Adoption threshold — how much peer commitment a node needs before it signs on. A low mean threshold makes almost any local majority enough to convert a node; a high one requires near-unanimous partner buy-in, which stalls the cascade even on a dense network (Watts calls this the "cascade window").
Try pushing the threshold slider up while density stays low: the cascade reliably dies out after adopting only the seeds' direct partners. Then raise density with a low threshold and watch a small seed group convert the entire network in a handful of steps — the same tipping-point behaviour observed in real technology-diffusion and collaboration networks.