This paper explores the mobility of the highly educated young Greek scholars. This is made possible through a bibliometric analysis of the affiliation countries of scholars who have published in peer reviewed journals indexed in Scopus. Approximately half of the researchers are identified from publications covered in Scopus for the period 2000–2019. A general taxonomy model is followed for analysing scientific mobility using affiliation changes. The greatest share of researchers (78.3%) appear to be static (74.6% in Greece and 3.7% abroad), whereas the mobile researcher category (21.7%) is divided into migrants (8.9%)—researchers who have left their country of origin—and travellers (12.8%)—researchers who gain additional affiliations while maintaining affiliation with their country of origin. According to the findings, the majority and especially the researcher elite (90.5%) did not sever ties with their country of origin, Greece, but instead built a chain of affiliations that linked nations together. Such chains are represented as groups of countries (clusters), in which the scientific connections between different countries can be visualised. It can be reasoned that the majority of researchers (70.3%) have a tendency to publish to a group of countries with ‘traditionally’ significant scientific impact.