Consensus group decision making (CGDM) allows the integration within this area of study of other advanced frameworks such as Social Network Analysis (SNA), Social Influence Network (SIN), clustering and trust-based concepts, among others. These complementary frameworks help to bridge the gap between their corresponding theories in such a way that important elements are not overlooked and are appropriately taken into consideration. In this paper, a new influence-driven feedback mechanism procedure is introduced for a preference similarity network clustering based consensus reaching process. The proposed influence-driven feedback mechanism aims at identifying the network influencer for the generation of advices. This procedure ensures that valuable recommendations are coming from the expert with most similar preferences with the other experts in the group. This is achieved by adapting, from the SIN theory into the CGDM context, an eigenvector-like measure of centrality for the purpose of: (i) measuring the influence score of experts, and (ii) determining the network influencer. Based on the initial evaluations on a set of alternatives provide by the experts in a group, the proposed influence score measure, which is named the σ-centrality, is used to define the similarity social influence network (SSIN) matrix. The σ-centrality is obtained by taking into account both the endogenous (internal network connections) and exogenous (external) factors, which means that SSIN connections as well as the opinion contribution from third parties are permitted in the nomination of the network influencer. The influence-driven feedback mechanism process is designed based on the satisfying of two important conditions to ensure that (1) the revised consensus degree is above the consensus threshold and that (2) the clustering solution is improved.