  Steady technological advances are paving the way for the implementation of
the quantum internet, a network of locations interconnected by quantum
channels. Here we propose a model to simulate a quantum internet based on
optical fibers and employ network-theory techniques to characterize the
statistical properties of the photonic networks it generates. Our model
predicts a continuous phase transition between a disconnected and a
highly-connected phase characterized by the computation of critical exponents.
Moreover we show that, although the networks do not present the small world
property, the average distance between nodes is typically small.
