The stable operation of edge networks relies heavily on the robustness of the underlying infrastructure, whose operational status can be monitored in real time via edge sensors. With the growing number of sensors and increasing monitoring frequency, the dimensionality and volume of time series data have surged dramatically, leading to the problem of catastrophic forgetting. Moreover, due to limitations in infrastructure and environmental factors, edge networks are more prone to data missing issues, posing significant challenges to data processing and analysis. To address these challenges, we propose a time series anomaly detection model tailored for edge network infrastructure. Specifically, to handle missing data, a multi-scale graph-based node imputation method is introduced to recover the missing values in the sequences. In the spatial dimension, a replay-based incremental learning strategy is designed, which leverages graph compression to capture critical features in the sequences, enabling the model to learn new features while alleviating the forgetting problem dynamically. In the temporal dimension, we adopt a single-layer WaveNet architecture that utilizes dilated convolutions and depthwise separable convolutions to efficiently extract features from multivariate time series, thereby reducing computational overhead. Extensive experiments conducted on the SMD and SWaT datasets demonstrate that the proposed model, i.e., ADEI, achieves superior performance.