Comparison of fitness and popularity: fitness-popularity dynamic network model

Dynamic networks are ubiquitous in the world. So far, many dynamic network models have been developed in search of network growth mechanisms at the node and edge levels. Especially, a number of fitness models have been employed for analysis of fitness (i.e. a node's inherent ability or characteristics) and popularity effects on growing networks. However, these models are not suitable for comparing the magnitude of the fitness and popularity effects. We propose a statistical dynamic network model called a fitness-popularity dynamic network (FPDN) model, where fitness and popularity effects are on equal footing. These effects are estimated under the FPDN model and the estimation procedure are applied to the network data, Flickr following, Facebook wallpost, and arXiv citation. The estimates of the two effects seem to represent the characters of the three networks with noteworthy interpretations. It is interesting to see that the popularity of a node negatively affects the growth of the in-degree of the node for the arXiv citation network while the effect is positive for the other networks.