Topological study of the convergence in the Voter Model

INES CARIDI; SERGIO MANTEROLA; SEMESHENKO, VIKTORIYA; BALENZUELA, PABLO

Applied Network Science

Springer

Año: 2019

2364-8228

The voter model has been widely studied due to its simple formulation and attainable theoretical treatment. The study of the ?active links?, edges that connect nodes in dif- ferent states, has been a key element in the analysis of the convergence of the model. Typically, the density of active links, ρ, is used to characterize the system when ap- proaching to absorbing state. However, more information can be extracted from how the active links are distributed across the underlying network.In this paper we study the dynamics of active links in the voter model, from a per- spective of complex networks. This approach allows us to understand how the dynamics of the model is mapped in topological features of a dynamical network of active links. We found that certain topological properties of the Active Link Network show salient features related to the dynamics of the model. The Active Link Network goes from a state similar to the underlying random network in the initial state to extremely disassor- tative graph when the dynamics approaches to absorbing state. In this state, the active link network is dominated by ?star-like? motifs, where different opinions take different topological roles on the network. Thus, the Active Link Network shows some prop- erties which are distant from the hypothesis made by the current theoretical models, which assume there are no correlations among active links.