This paper introduces Multi-Hop Pooling, a novel graph neural network pooling method that leverages transition matrices to capture multi-scale structural information. Unlike existing approaches that focus on either local or global graph properties, our method employs transition matrix powers to identify significant patterns across multiple hop distances. By explicitly modeling information propagation at different scales, we capture complex structural relationships that combine both local and global perspectives. Extensive experiments on seven benchmark datasets demonstrate that our method consistently outperforms state-of-the-art pooling approaches, with particularly significant improvements on molecular graphs where long-range interactions are crucial. Ablation studies confirm that incorporating multi-hop transition information substantially enhances pooling effectiveness. Our work bridges graph theory and neural architectures to develop more expressive hierarchical graph representations for improved graph classification.