Mapping the $q$-voter model: From a single chain to complex networks

TL;DR

This paper explores six different methods to map the modified q-voter model onto various complex networks, analyzing how the choice of influence group affects macroscopic behavior across different network types.

Contribution

It introduces and compares multiple mapping approaches for the q-voter model on diverse network topologies, highlighting the impact of network structure on model dynamics.

Findings

Mapping differences depend on network average path length

For real Twitter networks, mapping choices have minimal impact

Network topology influences the macroscopic behavior of the model

Abstract

We propose and compare six different ways of mapping the modified $q$-voter model to complex networks. Considering square lattices, Barab\'asi-Albert, Watts-Strogatz and real Twitter networks, we ask the question if always a particular choice of the group of influence of a fixed size $q$ leads to different behavior at the macroscopic level. Using Monte Carlo simulations we show that the answer depends on the relative average path length of the network and for real-life topologies the differences between the considered mappings may be negligible.