Perturbation Theory of Online User Dynamics with Respect to Change in Social Network Structures

Online user dynamics have become significant factors in considering issues in the stable operation of communication systems. Therefore, understanding the causal relationship between online user dynamics and the structure of networks would help provide significant information to ensure the system's stability. The oscillation model helps to understand the characteristics of online user dynamics in a purely theoretical framework. In the oscillation model, perturbation theory has been deployed to understand the effects of changes in network structure on online user dynamics. The perturbation theory examines changes in the solution when the network model changes slightly, starting from a known solution obtained from a model with well-known properties. In past studies, the perturbation theory has considered the changes in network structure as those in oscillation modes. However, we need a description of the change in the solution for changes in the network structure, not for those in the oscillation modes. This paper discusses perturbation theory, which describes changes in online user dynamics when the network structure changes, and shows that the treatment of perturbation theory is simplified for network structure changes that do not involve nodal degree changes.