Classification of higher education institutions (HEIs) of a country allows viewing higher education as a differentiated system which respects the diversity of purposes and aspirations of different HEIs. Classification is fundamentally different from ranking, which aims to rank universities in order with higher ranked HEIs being "better" than lower ranked ones. In classification, the universities in a class are grouped by their purpose and mission, and no attempt is made to rank them. Carnegie Classification of universities in the USA is the oldest classification system, which groups universities into a few categories like Research Universities, Masters Universities, Baccalaureate Universities, and Secondary. This classification has been found extremely useful over decades for various purposes including policy making and planning. This has thus motivated similar exercises in many other countries, particularly for research universities. In this paper, we evolve an approach to classify research universities in India, based on the Carnegie Classification approach. We propose a simple basic criterion for identifying research universities, and apply it to the top 100 universities and top 100 engineering institutions in India. Using this criteria, 40 universities and 32 engineering institutions were identified as research HEIs. Based on the data on the level of research activity in these HEIs, we apply a clustering approach similar to the one Carnegie uses to group research HEIs into two sub-categories, viz. "highest research activity" and "moderate research activity". The clustering approach identified six universities and eight engineering institutions in India to be in the highest research activity category. The level of research activity uses data on the number of full time PhD students, the number of faculty, research grants, and publications.