Migration of talent is a major driver of innovation. Large-scale bibliometric data have been used to measure international mobility of scholars. Yet, our understanding of internal migration among researchers is quite limited partly due to lack of data aggregated at a suitable sub-national level. In this study, we present a novel method and re-purpose bibliometric data using a neural network which provides a sub-national level for aggregating affiliation data. We analyze internal mobility based on over 1.3 million authorship records from the Scopus database to trace internal movements of over 150,000 scholars in Mexico and provide measures of internal migration such as net migration rates for all states over the period 1996-2019. Internal mobility is a rare event of a specific subset of active scholars. We document a core-periphery structure in the migration network of scholars' states centered around Mexico City, State of Mexico, Hidalgo, Morelos, and Queretaro which account for a major share of the total inter-state scholarly migration flows. Over the past two decades, the migration network has become more dense, but also more diverse, including greater exchange between states along the Gulf and the Pacific Coast. Our analysis of mobility events as a temporal network suggests that Mexican scholarly migration is experiencing a mobility transition in which migration between urban centers is increasing in particular to and from a single metropolitan region.