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Barabási & Albert 1999: Scale-Free Networks

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Barabási & Albert 1999: Scale-Free Networks

System notes

Real networks grow by preferential attachment: new nodes connect to existing nodes with probability proportional to their current degree.

The Barabási-Albert model analytically produces a power-law degree distribution P(k) ~ k⁻³ via mean-field continuum theory.

The Notre Dame web (325,000 pages, 1.5 million links) exhibits a power-law degree distribution with exponent γ ≈ 2.1.

Clauset, Shalizi, and Newman (2009) showed that most claimed real-world power-law networks fail rigorous statistical testing; many fit log-normal or exponential distributions better.

The Barabási-Albert model assumes undirected, unweighted, static networks; real networks have directionality, edge weights, multiplexity, and temporal decay.

Preferential attachment is one of multiple mechanisms that generate heavy-tailed degree distributions; copying models, fitness models, and optimization models also produce similar tails.

barabasi-1999 · condition map

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system
Real networks grow by preferential attachment: new nodes connect to existing nodes with probability proportional to their current degree.
sources: barabasi-1999
system
The Barabási-Albert model analytically produces a power-law degree distribution P(k) ~ k⁻³ via mean-field continuum theory.
sources: barabasi-1999
system
The Notre Dame web (325,000 pages, 1.5 million links) exhibits a power-law degree distribution with exponent γ ≈ 2.1.
sources: barabasi-1999
system
Clauset, Shalizi, and Newman (2009) showed that most claimed real-world power-law networks fail rigorous statistical testing; many fit log-normal or exponential distributions better.
sources: clauset-2009
system
The Barabási-Albert model assumes undirected, unweighted, static networks; real networks have directionality, edge weights, multiplexity, and temporal decay.
sources: barabasi-1999
2 more ranked claims
system0.80
Preferential attachment is one of multiple mechanisms that generate heavy-tailed degree distributions; copying models, fitness models, and optimization models also produce similar tails.
sources: barabasi-1999, clauset-2009
speculative0.70
Scale-free network topology is a fractal in connectivity space, sharing power-law mathematics with Mandelbrot's geometric scale invariance.
sources: mandelbrot-1967, barabasi-1999
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What does the ledger say about this (system tier): "The Barabási-Albert model analytically produces a power-law degree distribution P(k) ~ k⁻³ via mean-field continuum theory."?
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What does the ledger say about this (system tier): "The Notre Dame web (325,000 pages, 1.5 million links) exhibits a power-law degree distribution with exponent γ ≈ 2.1."?
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What does the ledger say about this (system tier): "Clauset, Shalizi, and Newman (2009) showed that most claimed real-world power-law networks fail rigorous statistical testing; many fit log-n…"?
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What does the ledger say about this (system tier): "The Barabási-Albert model assumes undirected, unweighted, static networks; real networks have directionality, edge weights, multiplexity, an…"?
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What does the ledger say about this (system tier): "Preferential attachment is one of multiple mechanisms that generate heavy-tailed degree distributions; copying models, fitness models, and o…"?
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