Percolation in neural networks

Abstract

The study of percolation transitions has proven useful to reveal information of the structure of complex networks, in particular living neuronal networks. Here we considered simulated neuronal networks and use inverse percolation, the process of erasing connections while keeping track of the size of the giant component g, to characterize their resilience to damage. We observed a phase transition in g, revealed by a sudden jump of g at a critical value for the connectivity of the network. We compared the behaviour of different network models (random and scale–free graphs) and different types of attack (damaging connections or neurons, random or targeted attack). We also investigated the critical exponent of the transition for a random graph.