Characterizing the intrinsic correlations of scalefree networks
Abstract
When studying topological or dynamical properties of random scalefree networks, it is tacitly assumed that degreedegree correlations are not present. However, simple constraints, such as the absence of multiple edges and selfloops, 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 scalefree 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 vertex on this vertices degree. Here, we introduce an analytical approach that is capable to predict the functional form of this property. Moreover, our results indicate that random scalefree network models are not selfaveraging, 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 scalefree networks.
 Publication:

International Journal of Modern Physics C
 Pub Date:
 August 2016
 DOI:
 10.1142/S0129183116500248
 arXiv:
 arXiv:1506.03289
 Bibcode:
 2016IJMPC..2750024D
 Keywords:

 Complex networks;
 intrinsic correlations;
 percolation;
 Physics  Physics and Society;
 Computer Science  Social and Information Networks
 EPrint:
 5 pages, 4 figures