The rise and fall of network stars: Analyzing 2.5 million graphs to reveal how high-degree vertices emerge over time

•We constructed the largest publicly available network evolution dataset to date, which contains 38,000 real-world networks and 2.5 million graphs.•Links are most prevalent among vertices that join a network at a similar time.•The rate that new vertices join a network is a central factor in molding a network’s topology.•The emergence of network stars (high-degree vertices) is correlated with fast-growing networks.•A novel flexible network-generation model based on large-scale real-world data is presented.