Self-organizing small-world networks are most robust against local disturbances

Small-world networks display enhanced signal-propagation speed, computational power, and synchronizability. Neuronal networks in the brain share properties of small-world networks and, in addition, dynamically rewire their connectivity by forming and deleting synapses. It is unclear whether small world networks are best in repairing damages caused by loss of connections and input. Neuronal networks show a reciprocal interaction between topology and the flow of neuronal (electrical) activity they generate. Topology determines the activity flow through the network, whereas on a longer timescale, the flow of activity requires new connections to be formed or existing ones to be removed. Importantly, neurons try to maintain their electrical activity at a certain setpoint (homeostasis of electrical activity). That is if neurons loose synaptic input due to a lesion, they respond with a local change in connectivity to obtain more activity from different sources. Here we investigate by a computational modelling study based on a model for activity-dependent structural plasticity [1,2], first, how local changes in synaptic connectivity alter global network topology after a circumscribed loss of input; and second, which topologies best support network repair re-establishing homeostasis in electrictal activity of all neurons. We found that reorganizing networks become more random as they form more long-range connections after a loss of input and those neurons loosing their input increase their centrality inbetweenness. Interestingly, an increased randomness and centrality inbetweenness has been recently found in functional connectivity of ipsilateral cortical and contralateral cerebellar networks following subcortical stroke [3]. As a second important result we found that small-world networks recover fastest (Fig.1) compared to regular and random networks from a loss of input in terms that all neurons return to homeostasis in electrical activity. The smallworldness of brain networks may therefore have an evolutionary advantage since those networks are more robust against lesions than regular (and random) networks.