Network intrusion detection systems (NIDSs) have emerged as a frontline defense against the potential attacks in the wireless Internet of Things (IoT) networks. However, existing machine learning methods follow an unstructured data processing patterns and can barely incorporate all information due to the network dynamicity as well as the data imbalance. In this study, we propose the graph isomorphism network model based on the edge (GINE), an innovative graph-based algorithm tailored to pinpoint the malicious network traffic within the wireless IoT networks. Specifically, we initiate by presenting the wireless IoT network graph, capturing the global topological interactions of its edges. Subsequently, we design an edge representation learning algorithm, capable of encoding network data frames in a discerning pattern-aware manner. Moreover, we integrate a data interpolation module into the edges of our structured graph data targeting at the data imbalance, which fosters a more balanced distribution across the various classes of edges. Our empirical analysis on the selected wireless IoT intrusion data sets shows GINE’s superiority, consistently outperforming the state-of-the-art methods in classification metrics, including accuracy, F1-score, false alarm rate, etc. Through a simulated wireless environment, we demonstrate GINE’s robust scalability, even in unpredictable wireless networks.