Poisson Edge Growth and Preferential Attachment Networks

When modeling a directed social network, one choice is to use the traditional preferential attachment model, which generates power-law tail distributions. In traditional directed preferential attachment, every new edge is added sequentially into the network. However, real datasets often have only coarse timestamps, which means several new edges are created at the same timestamp. Previous analyses on the evolution of social networks reveal that after reaching a stable phase, the growth of edge counts in a network follows a non-homogeneous Poisson process with a constant rate across the day but varying rates from day to day. Taking such empirical observations into account, we propose a modified preferential attachment model with Poisson edge growth, and study its asymptotic behavior. This new model is then fitted to real datasets using an extreme value estimation approach.