The efficiency of universities, which have a network structure of production process, is an essential component of performance measurement in education. However, most previous studies use traditional Data Envelopment Analysis (DEA), which disregards the network structure of the production process in universities. This study adopts a two-stage Network Data Envelopment Analysis (NDEA) with shared inputs model to assess the overall, teaching and research efficiencies of Turkish research universities. The findings show that only 6 out of 23 research universities are efficient, and some universities with lower world rankings are more efficient than those with higher rankings. On the other hand, no significant difference was found between the efficiency levels of regions with a high level of socio-economic development and regions with a relatively low level of socio-economic development. The study also evaluates the effects of different priority scenarios on efficiency and the optimal allocation of shared inputs between sub-processes. This study provides guidance for universities seeking to improve their performance and for the Council of Higher Education (CHE) in determining incentives for research universities. It also promotes the use of multi-stage NDEA with shared inputs model over traditional DEA for accurate efficiency assessment in the field of education.