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Spatial diversity assists parameter estimation in distributed networks. A sparsity-aware link combination strategy is proposed, which considers both the spatial sparsity in a network and the inherent sparsity of the system, where two types of zero-attracting adaptive combiners are proposed based on the least-mean-square the algorithm. The proposed algorithms exploit l1-norm regularisation through adaptive combination of neighbouring node weights such that the proposed algorithms can adaptively track the variations of the network topology. Simulation results illustrate the advantages of the proposed link combination algorithm in terms of convergence rate and steady-state performance for distributed sparse system learning. [ABSTRACT FROM AUTHOR]