IoT sensor networks have an inherent graph structure that can be used to extract graphical features for improving performance in a variety of prediction tasks. We propose a framework that represents IoT sensor network data as a graph, extracts graphical features, and applies feature selection methods to identify the most useful features that are to be used by a classifier for prediction tasks. We show that a set of generic graph-based features can improve performance of sensor network predictions without the need for application-specific and task-specific feature engineering. We apply this approach to three different prediction tasks: activity recognition from motion sensors in a smart home, demographic prediction from GPS sensor data in a smart phone, and activity recognition from GPS sensor data in a smart phone. Our approach produced comparable results with most of the state-of-the-art methods, while maintaining the additional advantage of general applicability to IoT sensor networks without using sophisticated and application-specific feature generation techniques or background knowledge. We further investigate the impact of using edge-transition times, categorical features, different sensor window sizes, and normalization in the smart home domain. We also consider deep learning approaches, including the Graph Convolutional Network (GCN), for the elimination of feature engineering in the smart home domain, but our approach provided better performance in most cases. We conclude that the graphical feature-based framework that is based on IoT sensor categorization, nodes and edges as features, and feature selection techniques provides superior results when compared to the non-graph-based features.