  Evolutionary game theory is employed to study topological conditions of
scale-free networks for the evolution of cooperation. We show that Apollonian
Networks (ANs) are perfect scale-free networks, on which cooperation can spread
to all individuals, even though there are initially only 3 or 4 hubs occupied
by cooperators and all the others by defectors. Local topological features such
as degree, clustering coefficient, gradient as well as topology potential are
adopted to analyze the advantages of ANs in cooperation enhancement.
Furthermore, a degree-skeleton underlying ANs is uncovered for understanding
the cooperation diffusion. Constructing this kind degree-skeleton for random
scale-free networks promotes cooperation level close to that of
Barab\'asi-Albert networks, which gives deeper insights into the origin of the
latter on organization and further promotion of cooperation.
