Preferential attachment

Preferential attachment is a generative mechanism for network growth in which new nodes entering a network tend to connect to existing nodes that already have high degree. Coined by Barabási and Albert in 1999 as the explanation for scale-free degree distributions, preferential attachment formalizes the intuitive rich-get-richer dynamic: well-connected nodes attract more connections because they are more visible, more accessible, or more useful.

The mechanism produces a power-law degree distribution with exponent γ = 3 in the simplest formulation, though modifications — fitness models, aging models, local search models — produce different exponents and cutoffs. Preferential attachment has been identified in scientific citation networks, hyperlink networks, airport route networks, and protein interaction networks, suggesting that it is not domain-specific but a general principle of network growth. The mechanism is closely related to Yule processes and Polya's urn models in probability theory, and to the Matthew Effect in sociology.