A temporal graph transformer neural network for clustering influential control nodes in the controllability processes on of social internet of things networks

The controllability of Social Internet of Things (SIoT) networks becomes particularly challenging when the network topology evolves over time and relationships span multiple layers, including user-to-user, object-to-object, and cross user-object interactions. In this paper, we introduce a novel learning-based framework called the Temporal Graph Transformer Neural Network for Clustering the Influential Nodes (TGCIN), which reformulates the identification of influential control nodes as an unsupervised node clustering problem on a temporal SIoT network. Our approach integrates relation-aware spatial attention to capture structural dependencies within each time snapshot, and a GRU-based temporal encoder combined with self-attention to model how node influence evolves across consecutive time steps. A controllability-informed scoring function is then introduced, which fuses structural driver ranks derived from maximum matching, multi-relational degree centrality, and a temporal stability index computed from embedding trajectory variance. These enriched representations are finally fed into a centroid-based clustering module that partitions nodes into three distinct control roles: critical drivers, bridging relays, and peripheral nodes. Experimental results demonstrate that the proposed method consistently outperforms existing approaches, achieving an average accuracy of approximately 91% and an average F1-score of around 92% across all tested scenarios. Beyond raw performance, the model converges faster than competing methods, maintains competitive runtime even on large-scale graphs, and produces interpretable cluster distributions where critical nodes are few but precisely identified, bridging nodes form a clear intermediate group, and peripheral nodes make up the majority without swallowing higher-impact nodes.