In the rapidly evolving field of Heterogeneous Multi-access Edge Computing (HMEC), efficient task offloading plays a pivotal role in optimizing system throughput and resource utilization. However, existing task offloading methods often fall short of adequately modeling the dependency topology relationships between offloaded tasks, which limits their effectiveness in capturing the complex interdependencies of task features. To address this limitation, we propose a task offloading mechanism based on Graph Neural Networks (GNN). Our modeling approach takes into account factors such as task characteristics, network conditions, and available resources at the edge, and embeds these captured features into the graph structure. By utilizing GNNs, our mechanism can capture and analyze the intricate relationships between task features, enabling a more comprehensive understanding of the underlying dependency topology. Through extensive evaluations in heterogeneous networks, our proposed algorithm improves 18.6\%-53.8\% over greedy and approximate algorithms in optimizing system throughput and resource utilization. Our experiments showcase the advantage of considering the intricate interplay of task features using GNN-based modeling.

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