  Several growth models have been proposed in the literature for scale-free
complex networks, with a range of fitness-based attachment models gaining
prominence recently. However, the processes by which such fitness-based
attachment behaviour can arise are less well understood, making it difficult to
compare the relative merits of such models. This paper analyses an evolutionary
mechanism that would give rise to a fitness-based attachment process. In
particular, it is proven by analytical and numerical methods that in
homogeneous networks, the minimisation of maximum exposure to node unfitness
leads to attachment probabilities that are proportional to node fitness. This
result is then extended to heterogeneous networks, with supply chain networks
being used as an example.
