The field of graph representation learning and hyperbolic embeddings is rapidly evolving, with a focus on developing innovative methods to capture complex structural properties and semantic hierarchies. Recent research has explored the use of hyperbolic space to model hierarchical relationships and power-law structures in graphs, leading to improved performance in various downstream tasks. Additionally, there is a growing interest in addressing the challenges of heterophily and heterogeneity in graphs, with approaches that explicitly model high-order semantics and adaptively separate homophilic and heterophilic patterns. Noteworthy papers in this area include HyperPath, which proposes a knowledge-guided hyperbolic semantic hierarchy modeling approach for whole slide image analysis, and Metapath-based Hyperbolic Contrastive Learning, which uses multiple hyperbolic spaces to capture diverse complex structures within heterogeneous graphs. Other notable works include Discrepancy-Aware Graph Mask Auto-Encoder, which reconstructs discrepancy information of neighboring nodes during the masking process, and Relation-Aware Separation of Homophily and Heterophily, which introduces a novel contrastive learning framework to explicitly model high-order semantics of heterogeneous interactions.