  In these notes we study synchronizability of dynamical processes defined on
complex networks as well as its interplay with network topology. Building from
a recent work by Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)], we
use a simulated annealing algorithm to construct optimally-synchronizable
networks. The resulting structures, known as entangled networks, are
characterized by an extremely homogeneous and interwoven topology: degree,
distance, and betweenness distributions are all very narrow, with short average
distances, large loops, and small modularity. Entangled networks exhibit an
excellent (almost optimal) performance with respect to other flow or
connectivity properties such as robustness, random walk minimal first-passage
times, and good searchability. All this converts entangled networks in a
powerful concept with optimal properties in many respects.
