We use a saturated linear gradient dynamical network for finding an approxi
mate solution to the maximum clique problem. We show that for almost all in
itial conditions, any solution of the network defined on a closed hypercube
reaches one of the vertices of the hypercube, and any such vertex correspo
nds to a maximal clique. We examine the performance of the method on a set
of random graphs and compare the results with those of some existing method
s. The proposed model presents a simple continuous, yet powerful, solution
in approximating maximum clique, which may outperform many relatively compl
ex methods, e.g,, Hopfield-type neural network based methods and convention
al heuristics.