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We analyze the growth models for complex networks including preferentialattachment (A.-L. Barabasi and R. Albert, Science 286, 509 (1999)) and fitnessmodel (Caldarelli et al., Phys. Rev. Lett. 89, 258702 (2002)) and demonstratethat, under very general conditions, these two models yield the same dynamicequation of network growth, $\frac{dK}{dt}=A(t)(K+K_{0})$, where $A(t)$ is theaging constant, $K$ is the node's degree, and $K_{0}$ is the initialattractivity. Basing on this result, we show that the fitness model provides anunderlying microscopic basis for the preferential attachment mechanism. Thisapproach yields long-sought explanation for the initial attractivity, anelusive parameter which was left unexplained within the framework of thepreferential attachment model. We show that $K_{0}$ is mainly determined by thewidth of the fitness distribution. The measurements of $K_{0}$ in many complexnetworks usually yield the same $K_{0}\sim 1$. This empirical universality canbe traced to frequently occurring lognormal fitness distribution with the width$\sigma\approx 1$.

Preferential attachment mechanism of complex network growth: "rich-gets-richer" or "fit-gets-richer"?