The prosperity of ride-sharing services has rippled in the communities of GIScience, transportation, and urban planning. Meanwhile, road network structure has been analyzed from a network science perspective that focuses on nodes and relational links and aims to predictive models. However, limited empirical studies have explored the relationship between road network structure and ride-sharing accessibility through such perspective. This paper utilizes the spatial Durbin model to understand the relationship between road network structure and ride-sharing accessibility, proxied by Uber accessibility, through classical network measures of degree, closeness, and betweenness centrality. Taking the city of Atlanta as a case study, we have found in addition to population density and road network density, larger values of degree centrality and smaller values of closeness centrality of the road network are associated with better accessibility of Uber services. However, the effects of betweenness centrality are not significant. Furthermore, we have revealed heterogeneous effects of degree centrality and closeness centrality on the accessibility of Uber services, as the magnitudes of their effects vary by different time windows (i.e., weekday vs. weekend, rush hour in the morning vs. evening). Network science provides us both conceptual and methodological measures to understand the association between road network structure and ride-sharing accessibility. In this study, we constructed road network structure measures with OpenStreetMap, which is reproducible, replicable, and scalable because of its global coverage and public availability. The study resonates with the notion of cities as the set of interactions across networks, as we have observed time-sensitive heterogeneous effects of road network structure on ride-sharing accessibility.