Blockmodels with maximum concentration

There are many circumstances in which binary relations are defined between pairs of objects: in sociology there are social relations between people; in business there are trading relations between firms; in design there are functional dependencies between components. In all of these the clustering of objects into densely interconnected blocks reveals something of the structure of the system. In this paper a criterion is presented which permits the construction of blocks to be formulated as a quadratic programme. The method is applied to two illustrative cases: the pattern of elective choices by MBA students and the performance assessment of British universities. The method is shown to give results which are readily interpreted and, for the purpose of performance ranking, leads to a more realistic description of achievement.