Connectome of memristive nanowire networks through graph theory

Hardware implementation of neural networks represents a milestone for exploiting the advantages of neuromorphic-type data processing and for making use of the inherent parallelism associated with such structures. In this context, memristive devices with their analogue functionalities are called to be promising building blocks for the hardware realization of artificial neural networks. As an alternative to conventional crossbar architectures where memristive devices are organized with a top-down approach in a grid-like fashion, neuromorphic-type data processing and computing capabilities have been explored in networks realized according to the principle of self-organization similarity found in biological neural networks. Here, we explore structural and functional connectivity of self-organized memristive nanowire (NW) networks within the theoretical framework of graph theory. While graph metrics reveal the link of the graph theoretical approach with geometrical considerations, results show that the interplay between network structure and its capacity to transmit information is related to a phase transition process consistent with percolation theory. Also the concept of memristive distance is introduced to investigate activation patterns and the dynamic evolution of the information flow across the network represented as a memristive graph. In agreement with experimental results, the emergent short-term dynamics reveals the formation of self-selected pathways with enhanced transport characteristics connecting stimulated areas and regulating the trafficking of the information flow. The network capability to process spatio-temporal input signals can be exploited for the implementation of unconventional computing paradigms in memristive graphs that take into advantage the inherent relationship between structure and functionality as in biological systems.