The objective assessment of the prestige of an academic institution is a difficult and hotly debated task. In the last few years, different types of university rankings have been proposed to quantify it, yet the debate on what rankings are exactly measuring is enduring.To address the issue we have measured a quantitative and reliable proxy of the academic reputation of a given institution and compared our findings with well-established impact indicators and academic rankings. Specifically, we study citation patterns among universities in five different Web of Science Subject Categories and use the PageRank algorithm on the five resulting citation networks. The rationale behind our work is that scientific citations are driven by the reputation of the reference so that the PageRank algorithm is expected to yield a rank which reflects the reputation of an academic institution in a specific field. Given the volume of the data analysed, our findings are statistically sound and less prone to bias, than, for instance, ad-hoc surveys often employed by ranking bodies in order to attain similar outcomes. The approach proposed in our paper may contribute to enhance ranking methodologies, by reconciling the qualitative evaluation of academic prestige with its quantitative measurements via publication impact.