Information Relaxation is Ultradiffusive

Abstract: We investigate how the overall response to a piece of information (a story or an article) evolves and relaxes as a function of time in social networks like Reddit, Digg and Youtube. This response or popularity is measured in terms of the number of votes/comments that the story (or article) accrued over time. We find that the temporal evolution of popularity can be described by a universal function whose parameters depend upon the system under consideration. Unlike most previous studies, which empirically investigated the dynamics of voting behavior, we also give a theoretical interpretation of the observed behavior using ultradiffusion. Whether it is the inter-arrival time between two consecutive votes on a story on Reddit or the comments on a video shared on Youtube, there is always a hierarchy of time scales in information propagation. One vote/comment might occur almost simultaneously with the previous, whereas another vote/comment might occur hours after the preceding one. This hierarchy of time scales leads us to believe that the dynamical response of users to information is ultradiffusive in nature. We show that a ultradiffusion based stochastic process can be used to rationalize the observed temporal evolution.