Topological Properties of Neuromorphic Nanowire Networks

Abstract

Graph theory has been extensively applied to the topological mapping of complex networks, ranging from social networks to biological systems. Graph theory has increasingly been applied to neuroscience as a method to explore the fundamental structural and functional properties of human neural networks. Here, we apply graph theory to a model of a novel neuromorphic system constructed from self-assembled nanowires, whose structure and function may mimic that of human neural networks. Simulations of neuromorphic nanowire networks allow us to directly examine their topology at the individual nanowire-node scale. This type of investigation is currently extremely difficult experimentally. We then apply network cartographic approaches to compare neuromorphic nanowire networks with: random networks (including an untrained artificial neural network); grid-like networks and the structural network of C. elegans. Our results demonstrate that neuromorphic nanowire networks exhibit a small-world architecture similar to the biological system of C. elegans, and significantly different from random and grid-like networks. Furthermore, neuromorphic nanowire networks appear more segregated and modular than random, grid-like and simple biological networks and more clustered than artificial neural networks. Given the inextricable link between structure and function in neural networks, these results may have important implications for mimicking cognitive functions in neuromorphic nanowire networks.

Keywords: artificial neural networks; atomic-switch networks; complex networks; graph theory; nanowires; neuromorphic; structural connectivity; topology.