We propose a new heuristic for approximating the maximum clique problem based on a recently introduced deterministic annealing algorithm, which generalizes Waugh and Westervelt's cluster-competitive net. The approach is centered on a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a linearly constrained quadratic program. Preliminary experiments on random as well as standard benchmark graphs are presented which demonstrates the validity of the approach.