Data for this study were obtained in the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) from the Integrated System for Human Resource Management (SIAPE) and from the Integrated System for Financial Management (SIAFI). They were also derived from the management reports of 57 Brazilian federal universities. We evaluated the main determinants of the number of graduate programs and their average evaluation grade. It was observed that the region, the city's population, the year of foundation, and the number of undergraduate students and training of technicians have no significant influence. The number of programs depends on the progress of the careers of the professors, evaluated in terms of their qualifications and age. The number of technicians also contributes positively. It was observed that the best universities are those with a greater number of programs, which shows positive results from interdepartmental competition within the institution.