Decay Characteristics of User Dynamics in Online Social Networks

Users' interests in trends and news that are attracting attention on social media are generally not retained for a long time but decrease with time. The activity dynamics, such as the gradual fading of interests of users in the social network, have been described as the damped oscillation model in previous studies. Previous studies assumed a damping coefficient (which expresses the strength of damping of the oscillation) as a constant independent of the frequency, but it is known that the damping coefficient in the general oscillation phenomena depends on the frequency. In this study, we define two matrices (the Laplacian matrix and its square root matrix) which give the social network structure and consider possible characteristics of the decay rate that can be derived from natural assumptions concerning the network structure.