A Formal Treatment of Generalized Preferential Attachment and its Empirical Validation

Generalized preferential attachment is defined as the tendency of a vertex to acquire new links in the future with respect to a particular vertex property. Understanding which properties influence link acquisition tendency (LAT) gives us a predictive power to estimate the future growth of network and insight about the actual dynamics governing the complex networks. In this study, we explore the effect of age and degree on LAT by analyzing data collected from a new complex-network growth dataset. We found that LAT and degree of a vertex are linearly correlated in accordance with previous studies. Interestingly, the relation between LAT and age of a vertex follows different forms for different values of the age. We identified three different periods in the network’s lifetime where the relation between age and LAT is strongly positive, almost stationary and negative correspondingly.