Automated fact-checking aims to assess the truthfulness of text based on relevant evidence, yet verifying complex claims requiring multi-hop reasoning remains a significant challenge. We propose GraphCheck, a novel framework that converts claims into entity-relationship graphs for comprehensive verification. By identifying relation between explicit entities and latent entities across multiple paths, GraphCheck enhances the adaptability and robustness of verification. Furthermore, we introduce DP-GraphCheck, a two-stage variant that improves performance by incorporating direct prompting as an initial filtering step. Experiments on the HOVER and EX-FEVER datasets show that our approach outperforms existing methods, particularly in multi-hop reasoning tasks. Furthermore, our two-stage framework generalizes well to other fact-checking pipelines, demonstrating its versatility.