In order to measure the amount of different information in a system, entropy concept can be used. Graph entropy measures nodes’ contribution to the entropy of the graph. By this way, the influential actors can be identified. Due to this case, a new entropy-based method was proposed to identify the influential actors. Karcı entropy was applied to the social networks first time. The alpha parameter allowed us to combine many different conditions together when measuring in the network. The other important contribution of this paper is to predict the value of alpha parameter of Karcı entropy by using fuzzy logic. After that Karcı and Shannon entropies were compared based on experimental results. Moreover, Karcı entropy was compared to traditional centrality measures. If Karcı entropy definition is considered as a set of entropies, Shannon entropy can be regarded as an element of this set. Accordingly, it can be concluded that Karcı entropy is superior to Shannon entropy.