Topological indices are indispensable tools for analyzing networks to understand the underlying topology of these networks. Spiking neural network architecture (SpiNNaker or TSNN) is a million-core calculating engine which aims at simulating the behavior of aggregates of up to a billion neurons in real time. Tickysim is a timing-based simulator of the interchip interconnection network of the SpiNNaker architecture. Tickysim spiking neural network is considered to be highly symmetrical network classes. Classical degree-based topological properties of Tickysim spiking neural network have been recently determined. Ev-degree and ve-degree concepts are two novel degrees recently defined in graph theory. Ev-degree and ve-degree topological indices have been defined as parallel to their corresponding counterparts. In this study, we investigate the ev-degree and ve-degree topological properties of Tickysim spiking neural network. These calculations give the information about the underlying topology of Tickysim spiking neural network.