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Flaming phenomena represent the divergence in the strength of user dynamicsas created by user interactions in online social networks (OSNs). Although ithas been known that flaming phenomena occur when the Laplacian matrix of theOSN has non-real eigenvalues, it was recently shown that flaming phenomena mayoccur even if all the eigenvalues are real numbers. This effect appears only inthe situation that some eigenvalues are degenerate, and a special unitarytransformation is applied to the equations representing user dynamics; whetheractual 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 isone specific example of the above condition. We also investigate the mechanismand characteristics of flaming phenomena generated by degenerated eigenvalues.Furthermore, we demonstrate through numerical simulations that the degenerationof eigenvalues can cause divergence.

Evaluation of User Dynamics Created by Weak Ties among Divided Communities