(A) study on the effects of fitness and popularity on network dynamics

Abstract

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. We also investigate the FPDN model under general fitness distribution.

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.

We applied the fitness and popularity in a Community Question Answering (CQA) websites, which are widely used in sharing knowledge. So far, the evaluation of answers has been explained by the contents of answers through the investigation of user's topics of interest and expertise levels. In this paper, we focus on the user behavior that users can see the answerer's profile as well as the answer's content before evaluating the quality of the answer. We propose the Popularity-based Topical Expertise Model (PTEM), a generative model which concerns the rich-get-richer phenomenon that popular user's answers are more recommended. We can simultaneously estimate the topical expertise of users and the size of the rich-get-richer effect through the EM algorithm combined with collapsed Gibbs sampling. Experiments on six fields of StackExchange community are performed. We observe the rich-get-richer phenomenon in every field, and the strengths are different over fields. We discuss the superiority and usefulness of the model through the study on the philosophy field.