Building Graphs at Scale via Sequence of Edges: Model and Generation Algorithms

Real-world graphs exhibit many interesting properties that differentiate them from random graphs, which have been extensively studied for the past decades. For various proposed generative models, a majority of them build the graph by sequentially adding each node and the attached edges. However, the growth of many real-world graphs, such as social networks, is naturally modeled by the sequential insertion of edges. Unfortunately, to the best of our knowledge, no generative model has been proposed to reveal this process. We propose the first sequence-of-edges model, denoted as temporal preferential attachment (TPA). It relies on preferential attachment (PA), one of the most influential mechanisms to generate scale-free graphs, and takes time-decay effect and node fitness into consideration. Empirical analysis demonstrates that our model preserves several key properties of the real-world graphs, including both the properties observed from the snapshot graphs (e.g., power-law distribution) and temporal properties observed from the graph generation process (e.g., shrinking diameter). Meanwhile, our model is sufficiently general to accommodate several forms of time decay and fitness distributions. Then, we design two efficient algorithms that generate TPA graphs with billions of edges in several minutes.