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In the area of the link mining, frequent pattern discovery tasks generally consist in the search for subgraphs frequently found in a network or a set of networks. Very recently, new axes of this problem has been proposed through the search for frequent links. Unlike traditional approaches that focus solely on structural regularities, frequent link mining methods exploit both the network structure and the attributes of nodes for extracting regularities in the links existing between node groups that share common characteristics. However, extracting frequent links is still a particularly challenging and computationally intensive issue since it is much dependent on the number of links. In this study, we propose a solution that is able to reduce the computing time by reducing the search to only a subset of of nodes. Experiments were conducted to understand the effects of different thresholds of the subset size on the loss of patterns and the gain in terms of computation time. Our solution proves to be efficient for a rather wide range of thresholds.