Topological study of the convergence in the Voter Model

INÉS CARIDI; SERGIO MANTEROLA; PABLO BALENZUELA

Cambridge

Conferencia; The 7th International Conference on Complex Networks and Their Applications; 2018

The Voter Model has been extensively studied due to its simple formulation and theoretical capabilities. The study of the ?active links?, those edges which link nodes in a different state, has been a key element in the analysis of the model. Typically, the density of active links, ρ, is used to characterize the approach to equilibrium. In this work, we study the process of convergence to equilibrium via the analysis of the topological properties of what we call the ?Active Link Network? (ALN). We found that the ALN goes from a state similar to the underlying random network in the initial state to one extremely disassortative when the dynamics approaches to equilibrium. In this state, the ALN is dominated by ?star-like? motifs, where different opinions play different topological roles on the network.