Transcutaneous auricular vagus nerve stimulation (taVNS) is a novel non-invasive brain stimulation technique considered as a potential supplementary treatment option for a wide range of diseases. Although first promising findings were obtained so far, the exact mode of action of taVNS is not fully understood yet. We recently developed an examination schedule to probe for immediate taVNS-induced modifications of large-scale epileptic brain networks. With this schedule, we observed short-term taVNS to have a topology-modifying, robustness- and stability-enhancing immediate effect on large-scale functional brain networks from subjects with focal epilepsies. We here expand on this study and investigate the impact of short-term taVNS on various local and global characteristics of large-scale evolving functional brain networks from a group of 30 subjects with and without central nervous system diseases. Our findings point to differential, at first glance counterintuitive, taVNS-mediated alterations of local and global topological network characteristics that result in a reconfiguration of networks and a modification of their stability and robustness properties. We propose a model of a stimulation-related stretching and compression of evolving functional brain networks that may help to better understand the mode of action of taVNS.