On the analysis of fitness change: fitness-popularity dynamic network model with varying fitness

There are various dynamic networks around us. Many researchers have investigated the fitness, i.e. ability to get edges from other nodes, and popularity effects on network growth. The fitness-popularity dynamic network (FPDN) model was introduced recently. In the FPDN model, the fitness of a node is assumed invariant for a given period of time. In many real networks, however, the fitness may change over time in various ways. Herein, we propose a varying fitness-popularity dynamic network (V-FPDN) model by allowing variable fitness. Through the V-FPDN model, we can estimate the strength of fitness and popularity effects and show how the fitness of the nodes changes. The magnitude of these effects and fitness values are estimated simultaneously using the expectation-maximization (EM) algorithm combined with the Markov chain Monte Carlo (MCMC) method. We apply the FPDN and V-FPDN model to the Facebook wallpost network and compare the results. The YouTube subscription network is investigated using the V-FPDN model in various categories. We explain the superiority of the proposed model with remarkable interpretations.