The network concept is widely applied for the description of amorphous materials, e.g., in the context of bonding topology, entanglement, gelation, jamming, etc., aspects that are all synonymous with mechanical stiffness. However, similar geometric criteria must characterize the migration pathways of mobile modifier cations, as these are delineated by the network structure. Hence, juxtaposing these antithetical glass properties can potentially reveal new insights into the amorphous state of matter. Indeed, we have shown how the adiabatic elastic modulus determined using Brillouin scattering, a technique that probes the nano-scale, serves to derive building block speciation in mixed network former glasses. Furthermore, the adiabatic bulk modulus and the activation energy for modifier cation migration are strongly anti-correlated, which led to an improved transition state theory model for cation hopping in glasses. By integrating MD simulations with this characterization approach, we endeavor to derive materials design criteria for amorphous solid-state electrolytes. Funding: NSF-DMR_1610742.