Continual graph learning (CGL) maintains models as graphs evolve without retraining from scratch, while mitigating catastrophic forgetting. Existing methods typically target either transductive or inductive settings and often store past subgraphs or require task identifiers at inference. We propose Community-aware Prototype Extraction for Continual Graph Learning (CoPE-CGL), a replay-free framework that uses a parameter-free structural prior, precomputed by multi-hop Laplacian smoothing, to anchor learning, memory, and inference. CoPE-CGL combines topology-infused bottleneck adaptation, community-level prototypes, and dynamic routing by majority vote over node-to-prototype matches. The default protocol assumes each test graph comes from one learned task; a node-level variant handles mixed-task graphs. Each task adds at most a constant amount of storage, with no past graph data retained. At equal storage and without task identifiers, CoPE-CGL matches the strongest replay baseline even when it receives true task identifiers: average performance (AP) is 95.17% and 95.72% versus 94.28% and 95.82% on Arxiv and CoraFull, respectively, with 5.9-14.0 times faster runtime and zero forgetting. Across four transductive and three inductive benchmarks and mixed streams, CoPE-CGL exceeds the second-best of up to eleven baselines by up to 1.41, 6.32, and 9.33 AP percentage points, respectively. It runs 1.3-7.9 times faster end-to-end than the most accurate competitor on each benchmark and scales to the largest benchmark graph. On graphs mixing two tasks, its node-level variant achieves the best AP among CGL methods. The design targets homophilic graphs with community structure.

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