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.
Highlights
Graph theory is a framework used to represent complex networks mathematically, whereby network components are represented as nodes (N) and connections between components are represented as edges (E) (Boccaletti et al, 2006)
We previously introduced a novel neuromorphic system comprised of self–assembled nanowires whose structure and function mimic that of biological neural networks (Kuncic et al, 2018; Diaz-Alvarez et al, 2019)
We compared the structures of multiple unique Atomic Switchlike Networks (ASNs) across four sizes with a fully-connected Artificial Neural Network (ANN), a C. elegans network, and Watts-Strogatz random/grid-like networks across four sizes and 21 varying β parameters
Summary
Graph theory has largely been employed to study the structure of networks, known as structural connectivity Measures such as the path length (PL), clustering coefficient (CCoeff ), participant coefficient (PCoeff ), withinmodule degree z-Score (MZ), degree and small worldness (see Box 1 for definitions), are useful. Within-Module Degree z-Score (MZ): Measures how well connected a node is to other nodes in the same module (or cluster/community) This demonstrates whether the node is a hub in the network (i.e., much of the information flows through this node) (Guimerà and Amaral, 2005). Small–worldness: A type of network architecture in which local clustering is combined with short path length This architecture offers important advantages for network functionality, ranging from synchronizability to information flow (Oliveira et al, 2014; Muldoon et al, 2016). Small–world Propensity: Introduced by (Muldoon et al, 2016), used to account for potential variations in connection strength in a network, by measuring how clustering and path length differ from random and grid-like networks
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