Statistically consistent coarse-grained simulations for critical phenomena in complex networks

TL;DR

This paper introduces a degree-based coarse graining method for complex networks that accelerates simulations while maintaining accuracy for both equilibrium and nonequilibrium dynamics, validated on Ising and epidemic models.

Contribution

The authors develop a new coarse graining approach that ensures statistical consistency and accurately captures phase transitions in complex network dynamics.

Findings

Coarse-grained networks replicate phase transition points of original networks.

The method satisfies equilibrium and nonequilibrium consistency conditions.

Numerical results show good agreement with original network dynamics.

Abstract

We propose a degree-based coarse graining approach that not just accelerates the evaluation of dynamics on complex networks, but also satisfies the consistency conditions for both equilibrium statistical distributions and nonequilibrium dynamical flows. For the Ising model and susceptible-infected-susceptible epidemic model, we introduce these required conditions explicitly and further prove that they are satisfied by our coarse-grained network construction within the annealed network approximation. Finally, we numerically show that the phase transitions and fluctuations on the coarse-grained network are all in good agreements with those on the original one.