Detecting anomalous data on IoT sensor network is an essential yet challenging task, especially if anomalies have small deviations from normal data, which would be more difficult in the coming 5G and beyond era due to the explosive growth of data. In this paper, the sensor data, as well as the network structural information, are studied to develop a robust and effective anomaly detection algorithm. The sensor data reconstruction model is built based on the recently developed nonlinear polynomial graph filter (NPGF), which involves the adjacency matrix of the sensor network and hence would learn from the network structural information. It first estimates the NPGF based reconstruction model from normal sensor data, and then detects anomalous sensors as those attaining high reconstruction error from the model. The proposed algorithm is shown to achieve 0.1 higher detection rate on anomalies with small deviations, compared with another recent graph-based detector based on linear graph frequency.