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