Conventional modelling of networks evolving in time focuses on capturing variations in the network structure. However, the network might be static from the origin or experience only deterministic, regulated changes in its structure, providing either a physical infrastructure or a specified connection arrangement for some other processes. Thus, to detect change in its exploitation, we need to focus on the processes happening on the network. In this work, we present the concept of monitoring random Temporal Edge Network (TEN) processes that take place on the edges of a graph having a fixed structure. Our framework is based on the Generalized Network Autoregressive statistical models with time-dependent exogenous variables (GNARX models) and Cumulative Sum (CUSUM) control charts. To demonstrate its effective detection of various types of change, we conduct a simulation study and monitor the real-world data of cross-border physical electricity flows in Europe.

翻译：传统时变网络建模侧重于捕捉网络结构的变化。然而，网络可能自始即保持静态，或仅经历确定性、受规制的结构变化，从而为其他过程提供物理基础设施或特定连接配置。因此，为检测网络利用方式的变化，须聚焦于网络上发生的过程。本文提出对固定结构图边上的随机时序边网络（TEN）过程进行监测的概念。我们的框架基于带时变外生变量的广义网络自回归统计模型（GNARX模型）与累积和（CUSUM）控制图。通过模拟研究以及对欧洲跨境物理电力流真实数据的监测，我们验证了该方法对各类变化模式的有效检测能力。