Strategic research direction and prioritisation is crucial for decision making in universities. Analysis of research diversification and sophistication helps differentiating universities according to their research attributes. Based on the Microsoft Academic Graph data set, this paper conducts research complexity analysis for all Australian universities, and examines the ubiquity and diversity of the research output. This paper also investigates research complexity indices of Australian universities, with further discussions for universities with research leadership, technological and practical focuses, and young research universities.