Thesis

Correlations In Scale-Free Networks

Bruno Miguel Tavares Gonçalves
Departamento de Física
Universidade de Aveiro

Abstract:

The study of connectivity correlations between nodes has been somewhat neglected in the study of Complex Networks. We try to correct this by using the correlation function, combined with the concept of shell to calculate the connectivity distribution, $P^{(d)}(k)$ and the average connectivity for the neighbours, $\langle k_{nn}^{(d)}(k)\rangle$ of a node as a function of distance

. With these results we create a better idea of how the Internet is organized and structured. We also determine that the time evolution of the Internet is coherent with the results obtained in the literature for the case of accelerated growth by the process of edge copying with a probability