This paper presents and describes the methodological opportunities offered by bibliometric data to produce indicators of scientific mobility. Large bibliographic datasets of disambiguated authors and their affiliations allow for the possibility of tracking the affiliation changes of scientists. Using the Web of Science as data source, we analyze the distribution of types of mobile scientists for a selection of countries. We explore the possibility of creating profiles of international mobility at the country level, and discuss potential interpretations and caveats. Five countries (Canada, The Netherlands, South Africa, Spain, and the United States) are used as examples. These profiles enable us to characterize these countries in terms of their strongest links with other countries. This type of analysis reveals circulation among and between countries with strong policy implications.