  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.
