Real academic networks (co-authorship, citation, conference circuits) are scale-free, not uniform: most professors have a handful of connections, but a small number of highly-cited "hub" professors accumulate dozens of long-range links across institutions. This simulator builds exactly that topology — a small hub clique fully interconnected (the conference circuit), each hub fanned out to many peripheral colleagues, and only a sparse scatter of direct peripheral-to-peripheral links (most researchers reach each other only through a hub intermediary).
degree distribution: P(k) ~ k^-γ (γ ≈ 2–3 for real citation nets)
hub degree: k_hub ≈ hubConnectivity (8–50)
peripheral degree: k_peri ≈ 2–4 (sparse, long-range)
per-contact infection: P(transmit) = p · dt (SI model, no recovery)
- Why hubs dominate spread — in a scale-free network the epidemic threshold collapses toward zero as hub degree grows (Pastor-Satorras & Vespignani, 2001): almost any transmission probability sustains an outbreak once it reaches a hub, because one hub infection creates dozens of simultaneous exposure events.
- Targeted vs. random immunization — removing/immunizing the highest-degree nodes is dramatically more effective than immunizing the same number of random nodes (Cohen, Erez, ben-Avraham & Havlin, 2000/2001, on scale-free network robustness). Try the "Hubs" vs "Random" buttons with the same hub count and compare the resulting spread rate.
- This is not the classroom model —
ufo-schoolchildren-pollution spreads through a dense, local, short-range classroom graph where every node has similar degree; here spread is dominated by a few long-range super-connectors, which is the defining feature of scale-free contagion.