Time translation symmetry breaking explains condensations in preferential attachment models[go to overview]
Time translation symmetry describes the property of a system that its physical laws are invariant under time shifting, as it is the case for the average node degree growths observed in the real network datasets we have examined. We propose a novel analytical framework for a general set of preferential attachment network models, where we express the network growth as an eigensystem. We show that the model explains the exponential network growth s = exp(σt) which is consistent with empirical findings, where the exponent σ can be determined by solving the eigenproblem. Conversely, the lack of solution of the eigenproblem corresponds to the breaking of the system’s time translation symmetry, which explains the winner-takes-all effect in some model settings, revealing the connection between the Bose-Einstein condensation in the Bianconi-Barabási model and similar gelation in superlinear preferential attachment. We prove that the aging effect is necessary to reproduce realistic node degree growth curves, and can prevent the winner-takes-all effect under weak conditions. Our results are verified by extensive numerical simulations.
12.03.20 - 10:15