Graph Neural Network Approach for Boundary Node Detection in Wireless Sensor and IoT Networks Using the LPCN Algorithm

Boundary node detection in wireless sensor networks (WSNs) and Internet of Things (IoT) networks is a fundamental problem with applications in perimeter surveillance, coverage verification, and network management. The Least Polar-angle Connected Node (LPCN) algorithm provides an exact solution by tracing the polygon hull of a connected Euclidean graph, but its distributed version (D-LPCN) requires sequential communication that is vulnerable to node failures and incompatible with dynamic networks. In this paper, we investigate whether a Graph Neural Network (GNN) can learn to approximate the LPCN boundary classification from data. We propose a complete methodology comprising: 1) automated generation of planar mesh networks, 2) extraction of 22 geometric and topological node features, 3) a message-passing GNN architecture with 3 propagation layers, and 4) a training data scaling study comparing models trained on 2K, 10K, and 100K networks. Comprehensive evaluation in 8 network configurations shows that the 100K-trained GNN achieves F1 = 0.992 in the training configuration and an average F1 = 0.963 in all settings, with perfect recall (zero missed boundary nodes) in 5 of 8 configurations. A real-world execution time analysis using ZigBee shows that D-LPCN requires ~1.2s for 50 nodes due to sequential communication, while the distributed GNN completes in ~141ms in parallel. We demonstrate that the GNN is fundamentally more robust to node failures and applicable to dynamic mobile networks where D-LPCN cannot operate. The 116 KB model runs entirely in-browser, enabling edge deployment without server infrastructure, as demonstrated by two companion web applications: an interactive step-by-step explainer of the complete pipeline and a real-time vehicle-tracking prototype operating on real OpenStreetMap road networks.