In recent years, social networks analysis has become a very active area of research. There has been a great focus of studying social networks in the area of graph theory. One important problem in social networks is the identification of the most influential actors which can be detected using different graph parameters. In this paper, we attempt to identify minimum sets of the most influential actors in trust social networks using weighted graphs with more focus on the critical nodes detection. We propose three methods: the first identifies the sets of the most important critical nodes using the concept of network efficiency; the second specifies conditions under which critical nodes should be controlled using connected components; and the third extracts sets of most powerful articulation points which are able to play critical nodes role. Computational results are demonstrated to confirm the effectiveness of our methods.