Fundamental framework for describing various node centralities using an oscillation model on social media networks

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In recent years, with the rapid development of the Internet and cloud computing, an enormous amount of information is exchanged on various social networking services. In order to handle and maintain such a mountain of information properly by limited resources in the network, it is very important to comprehend the dynamics for propagation of information or activity on the social network. One of many indices used by social network analysis which investigates the network structure is “Node centrality”. A common characteristic of conventional node centralities is that it depends on the topological structure of network and the value of node centrality does not change unless the topology changes. In our recent research, we have proposed an oscillation model for describing dynamics on networks generated from a certain kind of asymmetric interaction between nodes by using a symmetric matrix. Moreover, we proposed a new extended index of well-known two node centralities based on the oscillation model. In this paper, we discuss generally extension of node centralities based on the oscillation model. In addition, we show that the proposed index can describe various node centralities by properly assigning the weight of each link, and the proposed model is regarded as the fundamental framework for different node centralities.