Abstract The pre-Bötzinger complex (preBotC), located in the medulla, is the essential rhythm-generating neural network for breathing. The actions of opioids on this network impair its ability to generate robust, rhythmic output, contributing to life-threatening opioid-induced respiratory depression (OIRD). The occurrence of OIRD varies across individuals and internal and external states, increasing the risk of opioid use, yet the mechanisms of this variability are largely unknown. In this study, we utilize a computational model of the preBötC to perform several in silico experiments exploring how differences in network topology and the intrinsic properties of preBötC neurons influence the sensitivity of the network rhythm to opioids. We find that rhythms produced by preBötC networks in silico exhibit variable responses to simulated opioids, similar to the preBötC network in vitro . This variability is primarily due to random differences in network topology and can be manipulated by imposed changes in network connectivity and intrinsic neuronal properties. Our results identify features of the preBötC network that may regulate its susceptibility to opioids. Significance Statement The neural network in the brainstem that generates the breathing rhythm is disrupted by opioid drugs. However, this response can be surprisingly unpredictable. By constructing computational models of this rhythm-generating network, we illustrate how random differences in the distribution of biophysical properties and connectivity patterns within individual networks can predict their response to opioids, and we show how modulation of these network features can make breathing more susceptible or resistant to the effects of opioids.