Generalizing to unseen graph tasks without task-specific supervision remains challenging.Graph Neural Networks (GNNs) are limited by fixed label spaces, while Large Language Models (LLMs) lack structural inductive biases.Recent advances in Large Reasoning Models (LRMs) provide a zero-shot alternative via explicit, long chain-of-thought reasoning.Inspired by this, we propose a GNN-free approach that reformulates graph tasks-node classification, link prediction, and graph classification-as textual reasoning problems solved by LRMs.We introduce the first datasets with detailed reasoning traces for these tasks and develop GRAPH-R1, a reinforcement learning framework that leverages task-specific rethink templates to guide reasoning over linearized graphs.Experiments demonstrate that GRAPH-R1 outperforms state-of-the-art baselines in zero-shot settings, producing interpretable and effective predictions.Our work highlights the promise of explicit reasoning for graph learning and provides new resources for future research.Codes are available at https://github.com/lgybuaa/Graph-R1.