Scaling up real networks by geometric branching growth

Significance Branching processes underpin the complex evolution of many real systems. However, network models typically describe network growth in terms of a sequential addition of nodes. Here, we measured the evolution of real networks—journal citations and international trade—over a 100-y period and found that they grow in a self-similar way that preserves their structural features over time. This observation can be explained by a geometric branching growth model that generates a multiscale unfolding of the network by using a combination of branching growth and a hidden metric space approach. Our model enables multiple practical applications, including the detection of optimal network size for maximal response to an external influence and a finite-size scaling analysis of critical behavior.