Array spatial thinning is employed to select the most effective antenna elements in a large phased array for optimum performance concerning hardware and computational costs, in conjunction with managing element failure and radio interference mitigation. We formulate spatial array thinning under connectivity constraints to make the thinning applicable in large arrays. By introducing graph optimization, the problem is recast as a k-clique version of a generalized minimum clique problem. Furthermore, by studying optimum clustering for the proposed formulation, we show by an example that the unconstrained thinning performance is achievable, even with connectivity constraints.