Old gets richer: a growth model for the development of hubs

A wide range of biological and artificial networks have been shown to differ in many respects from purely random and regular networks. One such distinguishing characteristic is the presence of hubs, i.e. nodes which participate in a high number of connections. Often, this structural peculiarity goes hand in hand with a special functional role in the network. Therefore, a better understanding of how these hubs arise could shine light on their functional aspect. However, models that can explain the development of hubs, such as preferential attachment for scale-free networks or the duplication-divergence model, rely on non-local information exchange, which is problematic from a biological perspective.

Along these lines, we propose and characterise a simple and local model of network growth. We analyse several real-world datasets, e.g. neural connectivity of the C. elegans, macaque monkey and human, as well as protein interaction networks. We then demonstrate that our "non-linear growth model" is well in-line with the experimental observations, and so provides a general principle for hub development.