Pair approximation for the q-voter model with independence on complex networks

TL;DR

This paper applies pair approximation to analyze the q-voter model with independence noise on complex networks, deriving critical points and validating results with simulations, advancing understanding of nonlinear voter dynamics.

Contribution

It is the first application of pair approximation to nonlinear voter models with noise on complex networks, extending beyond complete graphs.

Findings

Pair approximation accurately predicts critical points for networks with weak clustering.

Discrepancies occur when the average degree is close to q.

Analytical results align with known solutions on fully connected networks.

Abstract

We investigate the q-voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derive a formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. The pair approximation prediction exhibits substantial agreement with simulations, especially for networks with weak clustering and large average degree. Nonetheless, for the average degree close to q, some discrepancies originate. It is the first time we are aware of that the presented approach has been applied to the nonlinear voter dynamics with noise. Up till now, the analytical results have been obtained only for a complete graph. We show that in the limiting case the prediction of pair approximation coincides with the known solution on a fully connected network.