In this paper, we propose a novel approach for the analysis of large-scale mobile telecommunications social networks. To search for alpha users that are essential for social marketing, we propose using both graph theory and linear algebra. In particular, we first look for all trusses in a social graph based on graph theory and then find out alpha users in the trusses based on linear algebra. While there is no proof that the adjacency matrix of a graph always has strictly positive eigenvectors, we prove that the adjacency matrix of a truss always has positive eigenvectors. The proposed approach is scalable and can be used to analyze massive networks.