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

TL;DR

This paper investigates the evolutionary mechanisms behind fitness-based attachment in network growth, demonstrating analytically and numerically that minimizing exposure to unfitness results in attachment proportional to node fitness, applicable to both homogeneous and heterogeneous networks.

Contribution

It provides a theoretical foundation explaining how fitness-based attachment behaviors can naturally emerge in network growth models.

Findings

Minimizing maximum unfitness exposure leads to fitness-proportional attachment.

Analytical and numerical methods confirm the emergence of fitness-based attachment.

Results extend from homogeneous to heterogeneous networks, including supply chains.

Abstract

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.