Recent studies have shown that social networks exhibit interesting characteristics such as community structures, i.e., vertexes can be clustered into communities that are densely connected together and loosely connected to other vertices. In order to identify communities, several definitions have been proposed that can characterize the density of connections among vertices in the networks. Dense triangle cores, also known as $k$-trusses, are subgraphs in which every edge participates at least $k-2$ triangles (a clique of size 3), exhibiting a high degree of cohesiveness among vertices. There are a number of research works that propose $k$-truss decomposition algorithms. However, existing in-memory algorithms for computing $k$-truss are inefficient for handling today’s massive networks. In this paper, we propose an efficient, yet scalable algorithm for finding $k$-trusses in a large-scale network. To this end, we propose a new structure, called triangle graph to speed up the process of finding the $k$-trusses and prove the correctness and efficiency of our method. We also evaluate the performance of the proposed algorithms through extensive experiments using real-world networks. The results of comprehensive experiments show that the proposed algorithms outperform the state-of-the-art methods by several orders of magnitudes in running time.