The research activity of individual universities has conventionally been measured by a number of bibliometric indicators based on the number of papers published in top-ranked journals or the number of citations they have received. Research funding is typically considered just one of several important input indicators, about on par with the number of researchers, that affect the research activities of universities. However, when we consider that competitive research funding applicants need to pass a rigorous screening by peers, the number and amount of accepted research funding proposals could be used as an output indicator for universities' research activities as well. The Grants-in-Aid for Scientific Research, which are provided by the Japanese Government, are the largest competitive external research funding source in Japan, and they play an extremely important role in helping researchers, especially at universities, undertake their work. In this study, we focus not only on the principal investigators but also on the co-investigators of funding applications to examine the indicators in university evaluation and research collaborations among universities.