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Phys Rev Lett. 2000 Nov 20;85(21):4633-6.

Structure of growing networks with preferential linking.

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Departamento de Física and Centro de Física do Porto, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal.


The model of growing networks with the preferential attachment of new links is generalized to include initial attractiveness of sites. We find the exact form of the stationary distribution of the number of incoming links of sites in the limit of long times, P(q), and the long-time limit of the average connectivity q(s,t) of a site s at time t (one site is added per unit of time). At long times, P(q) approximately q(-gamma) at q-->infinity and q(s,t) approximately (s/t)(-beta) at s/t-->0, where the exponent gamma varies from 2 to infinity depending on the initial attractiveness of sites. We show that the relation beta(gamma-1) = 1 between the exponents is universal.

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