To monitor risk in temporal financial networks, we need to understand how individual behaviours affect the global evolution of networks. Here we define a structural importance metric—which we denote as \(l_{e}\)—for the edges of a network. The metric is based on perturbing the adjacency matrix and observing the resultant change in its largest eigenvalues. We then propose a model of network evolution where this metric controls the probabilities of subsequent edge changes. We show using synthetic data how the parameters of the model are related to the capability of predicting whether an edge will change from its value of \(l_{e}\). We then estimate the model parameters associated with five real financial and social networks, and we study their predictability. These methods have applications in financial regulation whereby it is important to understand how individual changes to financial networks will impact their global behaviour. It also provides fundamental insights into spectral predictability in networks, and it demonstrates how spectral perturbations can be a useful tool in understanding the interplay between micro and macro features of networks.

为了监控临时金融网络中的风险，我们需要了解个人行为如何影响网络的全球演变。在这里，我们为网络的边缘定义了结构重要性度量标准，我们将其表示为\（l_ {e} \）。该度量基于扰动邻接矩阵并观察其最大特征值的结果变化。然后，我们提出了一种网络演化模型，其中该指标控制着后续边缘变化的可能性。我们使用合成数据显示模型的参数如何与预测边缘是否会从其\（l_ {e} \）值变化的能力相关联。然后，我们估计与五个实际财务和社交网络相关的模型参数，并研究它们的可预测性。这些方法在金融监管中都有应用，因此重要的是要了解金融网络的个人变化将如何影响其全球行为。它还提供了对网络频谱可预测性的基本见解，并演示了频谱扰动如何成为了解网络微观和宏观特征之间相互作用的有用工具。