A measure of centrality can be used to identify important assets that affect a system. In this study, the most used centrality measures degree, closeness, betweenness, eigenvector centrality and entropy centrality were used to identify the most effective nodes. The central/influential nodes can be detected more accurately by the Karci entropy which has just begun to be used new in social networks. Karci entropy contain Shannon when a equal 1. The more accurate results were obtained when the a coefficient in Karci entropy was correctly selected. The effect of node degree and edge weights to the network were measured together. The applicability of the entropy-based method for the detection of the most effective nodes in weighted networks has been demonstrated. The success of proposed method has been offered by comparison with traditional methods.