Community structures are critical for understanding the mesoscopic organization of networks, bridging local and global patterns. While methods such as DeepWalk and node2vec capture local positional information through random walks, they fail to preserve community structures. Other approaches like modularized nonnegative matrix factorization and evolutionary algorithms address this gap but are computationally expensive and unsuitable for large-scale networks. To overcome these limitations, we propose Two Layer Walk (TLWalk), a novel graph embedding algorithm that incorporates hierarchical community structures. TLWalk balances intra- and inter-community relationships through a community-aware random walk mechanism without requiring additional parameters. Theoretical analysis demonstrates that TLWalk effectively mitigates locality bias. Experiments on benchmark datasets show that TLWalk outperforms state-of-the-art methods, achieving up to 3.2% accuracy gains for link prediction tasks. By encoding dense local and sparse global structures, TLWalk proves robust and scalable across diverse networks, offering an efficient solution for network analysis.

翻译：社区结构对于理解网络的中观组织至关重要，它连接了局部与全局模式。虽然DeepWalk和node2vec等方法通过随机游走捕获局部位置信息，但它们无法保持社区结构。其他方法如模块化非负矩阵分解和进化算法虽能弥补这一不足，但计算成本高昂，不适用于大规模网络。为克服这些限制，我们提出了一种新颖的图嵌入算法——双层游走（TLWalk），该算法融入了层次化社区结构。TLWalk通过一种无需额外参数的社区感知随机游走机制，平衡了社区内与社区间的关系。理论分析表明，TLWalk能有效缓解局部性偏差。在基准数据集上的实验显示，TLWalk在链接预测任务中优于现有先进方法，准确率提升最高可达3.2%。通过编码稠密的局部结构与稀疏的全局结构，TLWalk在不同网络中均表现出鲁棒性和可扩展性，为网络分析提供了一种高效的解决方案。