Proposal of New Index for Describing Node Centralities Based on Oscillation Dynamics on Network

Since recent rapid development of information network technology activates the information exchange on the social network, dynamics for propagation of information or activity on the social network is an interesting research object. The network dynamics is generated by interaction between users whose strength is asymmetric in general. Network structure reflecting the asymmetric interaction between users is modeled by a directed graph, and it is described by an asymmetric matrix in matrix-based network model. 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. In this paper, based on the oscillation model, we propose a new extended index of the node centrality. The proposed index can describe various aspect of node centrality that considers not only the topological structure of the network, but also asymmetry of links, the distribution of source node of activity, and temporal evolution of activity propagation.