Optimizing device-to-device (D2D) topologies is pivotal for enhancing the performance and efficiency of 6G networks. This paper introduces a novel approach for forming optimal subnet trees within the  6G networks using BDIx agents and advanced Minimum-Weight Spanning Tree (MWST/MST) algorithms augmented by Graph Neural Networks (GNNs) and FeedForward Neural Networks (FFNN). Our solution aims to significantly boost network performance, particularly in high-demand scenarios such as urban areas, large-scale events, and remote locations. Our approach dynamically adapts to changing network conditions, user movements, and traffic patterns by minimizing power consumption and maximizing throughput. We implement various MWST algorithms, including Kruskal's, Prim's, and Boruvka's algorithms, and introduce a GNN model to predict edge weights combined with FFNNs to select parent nodes (called GNN-FFNN model), aiding in the construction of minimum-weight spanning trees (MWST). Additionally, a "weighted distance" metric is proposed to analyze network performance comprehensively. The proposed AI/ML-driven solution integrates BDIx agents with MWST algorithms, focusing on optimizing subnets under gNodeB in 6G networks, enhancing data transmission efficiency, reducing latency, and increasing throughput. This research contributes to developing scalable and flexible network management solutions suitable for diverse configurations and architectures.

Device-to-Device (D2D) communication, 6G networks, Minimum-Weight Spanning Tree (MWST), Graph Neural Networks (GNNs), BDIx agents, network optimization, power consumption, throughput, dynamic adaptation.,Feed