Network growth models: A behavioural basis for attachment proportional to fitness

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.

💡 Research Summary

The paper investigates the behavioural foundations of fitness‑based preferential attachment in growing complex networks. It proposes that agents aim to minimise the maximum exposure to “unfitness” – defined as the inverse of the total sum of node fitness values – and shows that this objective naturally yields attachment probabilities proportional to node fitness.

First, for homogeneous networks (where any node can connect to any other), the authors formulate a linear program that selects attachment probabilities (p_i) to minimise the expected network unfitness (E