Evaluation of User Dynamics Created by Weak Ties among Divided Communities

Flaming phenomena represent the divergence in the strength of user dynamics as created by user interactions in online social networks (OSNs). Although it has been known that flaming phenomena occur when the Laplacian matrix of the OSN has non-real eigenvalues, it was recently shown that flaming phenomena may occur even if all the eigenvalues are real numbers. This effect appears only in the situation that some eigenvalues are degenerate, and a special unitary transformation is applied to the equations representing user dynamics; whether actual OSNs satisfy this condition has not been fully discussed. In this paper, we clarify that the user dynamics caused by the degeneration of eigenvalue 0 is one specific example of the above condition. We also investigate the mechanism and characteristics of flaming phenomena generated by degenerated eigenvalues. Furthermore, we demonstrate through numerical simulations that the degeneration of eigenvalues can cause divergence.