Power Laws & Scale-Free Networks
Albert-László Barabási · 1999
"Barabási showed many real networks — the web, actor collaborations, protein interactions — are scale-free: a few hubs have vastly more links than average, following a power law produced by preferential attachment, not by bell-curve randomness."
Barabási mapped the web in 1999 expecting a bell curve and found a power law instead: a handful of pages have millions of links, most have almost none.
In a scale-free network, degree distribution follows P(k) ~ k^-γ; growth plus preferential attachment ('the rich get richer' — new nodes attach preferentially to already well-connected nodes) generates hubs. Consequences: scale-free networks are robust to random failure but fragile to targeted attack on hubs, and 'average node' is a misleading statistic — the median and the hub live in different worlds.
What structural feature defines a scale-free network?
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The explanation above is written with AI assistance. These are the originals — go to them to check it.
- Emergence of Scaling in Random Networks — power laws & scale-free networks (Barabási & Albert, 1999)Barabási & Albert / Wikipedia
Metcalfe's Law
"A network's value grows roughly with the square of its users, which is why the first users of a network are the hardest to get and the last are nearly free."