In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions' evolution. We explore the natural question of the large population limit with two approaches: the now classical mean-field limit and the more recent graph limit. After establishing the existence and uniqueness of solutions to the models that we will consider, we provide a rigorous mathematical justification for taking the graph limit in a general context. Then, establishing the key notion of indistinguishability, which is a necessary framework to consider the mean-field limit, we prove the subordination of the mean-field limit to the graph one in that context. This actually provides an alternative proof for the mean-field limit. We conclude by showing some numerical simulations to illustrate our results.

在本文中，我们研究了意见动态模型，其中代理的影响权重通过与意见演变相结合的方程随时间演变。我们用两种方法探索了大量人口限制的自然问题：现在的经典平均场限制和最近的图限制。在确定我们将考虑的模型的解的存在性和唯一性后，我们提供了严格的数学证明，以在一般情况下采用图限制。然后，建立不可区分性的关键概念，这是考虑平均场限制的必要框架，我们证明了平均场限制在该上下文中对图一的从属关系。这实际上为平均场极限提供了另一种证明。最后，我们通过展示一些数值模拟来说明我们的结果。