The Analysis of Popularity Effect on Network Dynamics
Hohyun Jung, Frederick Kin Hing PhoaThe popularity effect in a network, i.e., the phenomenon in which popular nodes become more popular, has been explained through the fitness models considering the node heterogeneity. The indegree has been regarded as node popularity, but the indegree does not always fully represent the popularity of nodes in real networks. The ``attractive" nodes, i.e., nodes with large fitness, are likely to have high popularity. When popularity is not given in a form of indegree, the interaction between fitness and popularity may not be considered, which may yield an inaccurate estimate of the fitness and popularity effects. In this study, we generalize the concept of fitness to capability and propose a capability-popularity dynamic network (CPDN) model. The CPDN model considers the interaction between the popularity and node heterogeneity when popularity is not expressed in indegree. Broad popularity and indegree processes can be covered in the framework of the proposed model. We present the EM algorithm combined with a Bayesian inference method to infer the node capability and static model parameters. Monte Carlo simulations are performed to show the validity of the CPDN model. We analyze the Twitch following and YouTube subscription networks and examine how the popularity effect works in the network growth with remarkable interpretations.