Oscillation Model for Network Dynamics Caused by Asymmetric Node Interaction Based on the Symmetric Scaled Laplacian Matrix

Since recent development and dissemination of ICTs activate information exchange on social networks, the dynamics for describing propagation of activities on the networks has became an interesting research object. This paper proposes an oscillation model describing the propagation of activities on social and information networks. In order to analyze such dynamics, we generally need to model asymmetric interaction between nodes. This paper discusses a symmetric matrix-based model that can describe some types of link asymmetry. Although the proposed model is simple, it can reproduce well-known indices of node centrality and can be considered as the underlying mechanism of network dynamics. As an application of the proposed model, we show a framework to estimate natural frequency of networks by utilizing resonance. Keywords—Laplacian matrix, coupled oscillators, node centrality, resonance