Analysis and applications of social networks with graph entropy

One of the concepts that provide criteria in complex structures is entropy. In this study, graph entropy was used to analyze social networks and their applications were shown. New methods were proposed for node centrality, one of the major problems of social networks. The ability of entropy to determine the centrality of network nodes was demonstrated. Entropy calculations were performed with Karcı entropy, Renyi entropy and Shannon entropy. Karcı entropy, which had never been used in social networks before, was applied to the social networks. A fuzzy α selection algorithm was proposed to determine the α value used in the Karcı entropy and Renyi entropy using density and clustering coefficient, which are the topological properties of the network. The proposed methods were applied to the Flags, Air Traffic, and Netscience data sets. Karcı entropy was compared with Renyi and Shannon entropies. The results of the analysis were compared with the traditional centrality measures which are degree, betweenness, closeness, and eigenvector centralities. The accuracy, effectiveness, and applicability of the proposed method were shown. Local and global measurements were performed. Karcı entropy and Renyi entropy were able to identify the influential actors in some complex systems where conventional methods cannot find a solution. The effect of node degrees and edge weights to the centrality could be measured together. New data sets were introduced to social networks.