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 different 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 approaching 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 perspective 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 disassortative 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 properties which are distant from the hypothesis made by the current theoretical models, which assume there are no correlations among active links.

中文翻译：

---

选民模型收敛的拓扑研究

由于其简单的表述和可达到的理论处理，投票者模型已得到广泛研究。连接不同状态节点的边“活动链接”的研究一直是分析模型收敛性的关键要素。通常，活动链接的密度ρ在接近吸收状态时用来表征系统。但是，可以从活动链接在基础网络中的分布方式中提取更多信息。本文从复杂网络的角度研究了选民模型中活动链接的动态。这种方法使我们能够了解如何将模型的动力学映射到活动链接的动态网络的拓扑特征中。我们发现，Active Link网络的某些拓扑属性显示出与模型动力学相关的显着特征。当动力学趋于吸收状态时，主动链路网络将从类似于初始状态下的基础随机网络的状态变为极端分散的图形。在这种状态下，主动链接网络以“星形”主题为主导，在网络上，不同的意见在拓扑中扮演着不同的角色。因此，活动链接网络显示出一些与当前理论模型所提出的假设相距甚远的属性，这些理论假设活动链接之间没有相关性。