The origin of degree correlations in the Internet and other networks

It has been argued that the observed anticorrelation between the degrees of adjacent vertices in the network representation of the Internet has its origin in the restriction that no two vertices have more than one edge connecting them. Here we introduce a formalism for modeling ensembles of graphs with single edges only and derive values for the exponents and correlation coefficients characterizing them. Our results confirm that the conjectured mechanism does indeed give rise to correlations of the kind seen in the Internet, although only a part of the measured correlation can be accounted for in this way.