  In this work we study the behavior of classical two-person, two-strategies
evolutionary games on a class of weighted networks derived from
Barab\'asi-Albert and random scale-free unweighted graphs. Using customary
imitative dynamics, our numerical simulation results show that the presence of
link weights that are correlated in a particular manner with the degree of the
link endpoints, leads to unprecedented levels of cooperation in the whole
games' phase space, well above those found for the corresponding unweighted
complex networks. We provide intuitive explanations for this favorable behavior
by transforming the weighted networks into unweighted ones with particular
topological properties. The resulting structures help to understand why
cooperation can thrive and also give ideas as to how such supercooperative
networks might be built.
