Multiplex Network Analysis of Local Topology in Simulated and \textit{In Vitro} Spiking Neural Networks

Complex networks are important tools for investigating interactions amongst many different types of agents. Recently, the extension of single layer networks to multilayer networks has allowed for multiple types of relationships among the same actors to be represented in a network. In this dissertation, we develop two methods for using a specific type of multilayer network, the multiplex network, to study local topology in neural networks. In the first project, we use multiplex networks to compare the local topology between a simulated structural neural network and its inferred functional networks. For the second project, we use multiplex networks to observe evidence for the self-organization of \textit{in vitro} neural networks into neural ensembles.Ph.D., Mathematics -- Drexel University, 201