Previous research has sought to enhance the graph reasoning capabilities of LLMs by supervised fine-tuning on synthetic graph data. While these led to specialized LLMs better at solving graph algorithm problems, we don't need LLMs for shortest path: we need generalization from synthetic graph data to real-world tasks with implicit graph structures. In this work, we propose to unlock generalizable learning of graph with post-training alignment with synthetic data. We first design solution-based and process-based rewards for synthetic graph problems: instead of rigid memorizing response patterns in direct fine-tuning, we posit that post-training alignment would help LLMs grasp the essentials underlying graph reasoning and alleviate overfitting on synthetic data. We employ post-training alignment algorithms such as GRPO and DPO, aligning both off-the-shelf LLMs and LLMs fine-tuned on synthetic graph data. We then compare them against existing settings on both in-domain synthetic tasks and out-of-domain real-world tasks with implicit graph structures such as multi-hop QA, structured planning, and more. Extensive experiments demonstrate that our post-training alignment recipe leads to statistically significant improvement on 5 datasets, with an average gain of 12.9% over baseline settings. Further analysis reveals that process-based rewards consistently outperform solution-based rewards on synthetic data but not on real-world tasks, and compositionality and explainable intermediate steps remains a critical challenge even after post-training alignment.