Rich get richer: new nodes attach to high-degree nodes, producing a power-law degree distribution
Network (node size ∝ degree, hubs highlighted)
Degree distribution (log-log)
Barabási-Albert model: start with m₀ nodes, add one node at a time, each connecting to m existing nodes with probability proportional to degree.
This "preferential attachment" rule produces a scale-free network with degree distribution P(k) ∝ k⁻³ (γ=3 for BA).
Hubs with degree ≫ average are inevitable. Erdős-Rényi random graphs have Poisson degree distributions — no hubs.
The BA model explains power-laws in the WWW, citations, social networks, and protein interactions.