Wireless sensor networks (WSNs) have become increasingly important in recent years due to their ability to monitor and collect data in various environments. However, WSNs often face limitations in terms of their energy resources, making energy efficiency a critical concern when designing WSNs. Clustering and multihop routing are effective methods for maximizing the lifetime of WSNs. The Graph Neural Network (GNN) is an emerging architecture in neural networks that has recently gained attention for solving problems in various domains, including wireless networks. In this paper, we propose a method based on GNN to create static clusters of equal size. This approach aims to balance energy consumption among the nodes, which is an important sub-goal in designing an energy-efficient WSN clustering protocol. Additionally, we introduce a distributed cluster head selection scheme that operates independently within each cluster. Another crucial aspect of energy efficiency in WSNs is multi-hop routing, which helps avoid long-distance communication that consumes significant amounts of energy. Our proposed centralized routing protocol establishes exclusive routes to the base station for each cluster. This ensures even energy consumption for relay nodes and prevents the hotspot problem. To evaluate our proposed protocol, we conducted simulations comparing it with several state-of-the-art counterparts. The empirical results demonstrate that our approach outperforms other protocols in terms of lifetime and coverage metrics.
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