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Existing methods particularly those based on experience replay typically store and revisit past graph data to mitigate catastrophic forgetting. However, these approaches pose significant limitations, including privacy concerns, inefficiency. In this work, we propose AL GNN, a novel framework for continual graph learning that eliminates the need for backpropagation and replay buffers. Instead, AL GNN leverages principles from analytic learning theory to formulate learning as a recursive least squares optimization process. It maintains and updates model knowledge analytically through closed form classifier updates and a regularized feature autocorrelation matrix. 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Instead, AL GNN leverages principles from analytic learning theory to formulate learning as a recursive least squares optimization process. It maintains and updates model knowledge analytically through closed form classifier updates and a regularized feature autocorrelation matrix. 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