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Graph theory within power electronics, developed over a 50-year span, is continually evolving, necessitating ongoing research endeavors. Facing with the never-been-seen explosion of graph-structured data, the state-of-the-art deep learning technique-Graph Neural Networks (GNNs), becomes the leading trend in machine learning within just recent five years and demonstrated surprisingly broad and prominent benefits covering from new drug discovery to better IC design. However, its promising applications in Power Electronics are still rarely discussed and its full potential remains unexplored. Addressing this gap, this review paper is the first to outline GNNs&#x2019; general workflow in power electronics, laying the groundwork and examining current GNN methodologies within the field. To bridge the gap in the sparse GNN literature within this domain, we also provide extended discussions on leveraging insights from GNN-aided circuit design to enrich power electronics research. Our work includes in-depth GNN-based case studies that demonstrate promising applications from converters to system-level power electronics, showcasing GNNs&#x2019; unique benefits and untapped possibilities (e.g., accurate component design, voltage predictions on IEEE-13 bus and 118 bus systems). Additionally, we provide a comprehensive survey of GNNs&#x2019; latest and successful applications, emphasizing their impact on energy-centric sectors, such as transportation electrification, smart grids. Considering the interdisciplinary nature of power electronics in modern energy systems, our review highlights the potential of GNNs emerge as a promising tool to decode the intricate behavior and dynamics of power electronics systems, and we hope such synergies between advanced AI methodologies like GNNs with the ever-evolving graph theory can lead to more powerful tools, novel methodologies, and advancements in the power electronics community.

From Graph Theory to Graph Neural Networks (GNNs): The Opportunities of GNNs in Power Electronics