Virtually all molecular interactions networks, independent of organism and physiological context, have majority-leaves minority-hubs (mLmH) topology. Current generative models of this topology are based on controversial hypotheses that, controversy aside, demonstrate sufficient but not necessary evolutionary conditions for its emergence. Here we show that the circumvention of computational intractability provides sufficient and (assuming P!=NP) necessary conditions for the emergence of the mLmH property. Evolutionary pressure on molecular interaction networks is simulated by randomly labelling some interactions as 'beneficial' and others 'detrimental'. Each gene is subsequently given a benefit (damage) score according to how many beneficial (detrimental) interactions it is projecting onto or attracting from other genes. The problem of identifying which subset of genes should ideally be conserved and which deleted, so as to maximize (minimize) the total number of beneficial (detrimental) interactions network-wide, is NP-hard. An evolutionary algorithm that simulates hypothetical instances of this problem and selects for networks that produce the easiest instances leads to networks that possess the mLmH property. The degree distributions of synthetically evolved networks match those of publicly available experimentally-validated biological networks from many phylogenetically-distant organisms.