We consider the heaviest subgraph problem, i.e. determine a block of k nodes of a weighted graph (of n nodes) such that the total edge weight within the subgraph induced by the block is maximized. We compare from a theoretical and practical point of view different mixed integer programming formulations of this problem. Computational experiments when the weight of each edge is equal to 1 are reported. Key words: Heaviest k-subgraph problem, mixed integer linear programming, upper bounds, experiments.