The possible correlation profiles of networks with a given scale-free degree distribution are restricted and bounded by maximally correlated configurations. Dissortative networks consist of nested bilayers, in which low-degree vertices are connected to high-degree vertices. The number of these bilayers attains a constant value for large network size $N$. Assortative networks exhibit monolayers of low-degree vertices, the number of which grows monotonously with $N$. Analytical relations for the Pearson correlation coefficient $r$ of these extremal configurations are derived and shown to provide lower and upper bounds on the possible $r$ values. Both bounds are found to vanish for large networks.

• Received 23 October 2009

DOI:https://doi.org/10.1103/PhysRevE.81.046103