Prove optimality of the FTL total rewiring for maximum assortativity

Establish whether the total-rewiring configuration produced by the Fast Total Link (FTL) degree-assortative rewiring procedure—constructed by ranking nodes by degree and connecting each node to the highest-degree available neighbors up to its original degree—achieves the maximum possible degree assortativity coefficient r among all simple graphs with the same degree sequence as the original network.

Background

The paper introduces the Fast Total Link (FTL) algorithm for degree-preserving rewiring aimed at rapidly tuning degree assortativity. A key step in the algorithm is a "total rewiring" that removes all edges and reconnects nodes in degree order to generate a highly assortative configuration before adjusting toward a target value via batch rewiring.

The authors observe empirically that this total rewiring yields very high assortativity and suggest it may even be optimal for a fixed degree sequence, but they explicitly note that they have not proven this. A formal proof (or counterexample) would characterize the extremal assortativity achievable under degree constraints and clarify the theoretical optimality of the FTL construction.