Successive whole genome duplications have recently been firmly established in all major eukaryote kingdoms. It is not clear, however, how such dramatic evolutionary process has contributed to shape the large scale topology of protein-protein interaction (PPI) networks. We propose and analytically solve a generic model of PPI network evolution under successive whole genome duplications. This demonstrates that the observed scale-free degree distributions and conserved multi-protein complexes may have concomitantly arised from i) intrinsic exponential dynamics of PPI network evolution and ii) asymmetric divergence of gene duplicates. This requirement of asymmetric divergence is in fact "spontaneously" fulfilled at the level of protein-binding domains. In addition, domain shuffling of multi-domain proteins is shown to provide a powerful combinatorial source of PPI network innovation, while preserving essential structures of the underlying single-domain interaction network. Finally, large scale features of PPI networks reflecting the "combinatorial logic" behind direct and indirect protein interactions are well reproduced numerically with only two adjusted parameters of clear biological significance.