🕸️ Scale-Free Network

The Barabási-Albert model (1999) grows a network by preferential attachment: each new node connects to m existing nodes with probability proportional to their current degree — "the rich get richer". This produces a power-law degree distribution P(k) ~ k^−γ with γ≈3, where a few highly connected hubs dominate. The same topology appears in the Internet, WWW, citation networks, social media and protein interaction networks. Click Grow to add nodes one by one, or Auto to watch continuous growth. Drag nodes to rearrange. 🇺🇦 Українська

Growth Controls

m (links/node) 2 Speed 5 nodes/s Max nodes 80

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Power-Law and Real Networks

In an Erdős-Rényi random graph, edges are placed uniformly at random — the degree distribution is Poisson and nodes are largely interchangeable. In a scale-free network, the degree distribution follows a power law: P(k) ∝ k^−γ, meaning very high-degree hubs exist with far higher probability than a Poisson distribution would predict. This makes scale-free networks robust against random failures (rare that a hub fails by chance) but vulnerable to targeted attacks (removing a few hubs fragments the network). The WWW (web pages → links), actor collaboration networks, and metabolic networks all show γ ≈ 2–3. The BA model gives γ = 3 exactly for any m.