Accuracy of Mean-Field Theory for Dynamics on Real-World Networks

TL;DR

This paper evaluates the accuracy of mean-field theory in predicting dynamics on real-world networks, revealing its dependence on network structure and degree correlations, and showing it can be surprisingly accurate even on sparse, disassortative networks.

Contribution

It systematically compares mean-field predictions with simulations on real networks, highlighting factors influencing accuracy and identifying conditions for reliable predictions.

Findings

Mean-field accuracy depends on mean degree and first-neighbor degree.

The theory performs well on disassortative networks with low mean degree.

Mean-field can be unexpectedly accurate even with sparse network structures.

Abstract

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for real-world networks with clustering and modular structure. In this paper, we compare mean-field predictions to numerical simulation results for dynamical processes running on 21 real-world networks and demonstrate that the accuracy of the theory depends not only on the mean degree of the networks but also on the mean first-neighbor degree. We show that mean-field theory can give (unexpectedly) accurate results for certain dynamics on disassortative real-world networks even when the mean degree is as low as 4.