International students are potential highly skilled workers who can enter in their host country's labor market. In Switzerland, migration policies regulate the selection criteria for migrant workers, including international students who subsequently seek employment after graduation. However, Switzerland has competing national interests: on the one hand, economic efficiency requires highly skilled workers who are partially recruited abroad; on the other hand, the state has to address concerns related to immigration, social cohesion, national identity, and security. We analyze the dynamic of international graduates' integration in the Swiss labor market. We first provide an overview of the stay rates of graduate students based on register data, and then we conduct a multivariate analysis of Swiss labor market integration based on graduate surveys from the Swiss Federal Statistical Office. We complement the analysis with responses to problems encountered by the international graduates when seeking employment. We find that Switzerland accesses a pool of variously skilled graduates upon their graduation from Swiss universities. While Swiss employers recruit both European and non-European graduates, the priority rule and facilitated mobility for EU nationals are reflected in higher employment rates of EU graduates. Graduates with degrees in science, technology, engineering, and math (STEM) are more likely than non-STEM graduates to find employment in Switzerland. Yet, this factor is not as strong as expected for all non-EU nationals: STEM graduates from both EU and non-EU countries, as well as the Asia-Pacific region, are employed at a significantly higher rate than non-STEM graduates from the same region.