Evaluation of User Dynamics Created by Weak Ties among Divided Communities

TL;DR

This paper investigates how eigenvalue degeneracy in the Laplacian matrix of online social networks can lead to flaming phenomena, revealing new conditions under which divergence in user dynamics occurs.

Contribution

It clarifies that eigenvalue degeneration, especially at zero, can induce flaming phenomena, extending understanding beyond previous eigenvalue-based conditions.

Findings

Degeneration of eigenvalue 0 causes user dynamics divergence.

Eigenvalue degeneracy can induce flaming phenomena.

Numerical simulations confirm divergence due to eigenvalue degeneration.

Abstract

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.