Numerous methods have been proposed in order to perform clustering from social networks. While significant works have been carried out on the design of new approaches, able to search for various kinds of clusters, a major challenge concerns the scalability of these approaches. Indeed, given the mass of data that can now be collected from online social networks, particularly from social platforms, it is important to have efficient methods for exploring and analyzing these very large amount of data. One of the recent social network clustering approaches is the extraction of conceptual links, a new approach that performs link clustering by exploiting both the structure of the network and attributes of nodes to identify strong links between groups of nodes in which nodes share common attributes. In this paper, we focus on the optimization of the search for conceptual links. In particular, we propose PALM, a parallel algorithm that aims to improve the efficiency of the extraction by simultaneously exploring several areas of the search space. For this purpose, we begin by demonstrating that the solution space forms a concept lattice. Then, we propose an approach that explores in parallel the branches of the lattice while reducing the search space based on various properties of conceptual links. We demonstrate the efficiency of the algorithm by comparing the performances with the original extraction approach. The results obtained show a significant gain on the computation time.