  Very often, when studying topological or dynamical properties of random
scale-free networks, it is tacitly assumed that degree-degree correlations are
not present. However, simple constraints, such as the absence of multiple edges
and self-loops, can give rise to intrinsic correlations in these structures. In
the same way that Fermionic correlations in thermodynamic systems are relevant
only in the limit of low temperature, the intrinsic correlations in scale-free
networks are relevant only when the extreme values for the degrees grow faster
than the square-root of the network size. In this situation, these correlations
can significantly affect the dependence of the average degree of the nearest
neighbors of a given vertice on this vertices's degree. Here, we introduce an
analytical approach that is capable to predict the functional form of this
property. Moreover, our results indicate that random scale-free networks models
are not self-averaging, that is, the second moment of their degree distribution
may vary orders of magnitude among different realizations. Finally, we argue
that the intrinsic correlations investigated here may have profound impact on
the critical properties of random scale-free networks.
