Generative models of rich clubs in Hebbian neuronal networks and large-scale human brain networks.

Rich clubs arise when nodes that are 'rich' in connections also form an elite, densely connected 'club'. In brain networks, rich clubs incur high physical connection costs but also appear to be especially valuable to brain function. However, little is known about the selection pressures that drive their formation. Here, we take two complementary approaches to this question: firstly we show, using generative modelling, that the emergence of rich clubs in large-scale human brain networks can be driven by an economic trade-off between connection costs and a second, competing topological term. Secondly we show, using simulated neural networks, that Hebbian learning rules also drive the emergence of rich clubs at the microscopic level, and that the prominence of these features increases with learning time. These results suggest that Hebbian learning may provide a neuronal mechanism for the selection of complex features such as rich clubs. The neural networks that we investigate are explicitly Hebbian, and we argue that the topological term in our model of large-scale brain connectivity may represent an analogous connection rule. This putative link between learning and rich clubs is also consistent with predictions that integrative aspects of brain network organization are especially important for adaptive behaviour.