The field of graph neural networks and topological methods is rapidly advancing, with a focus on developing innovative frameworks for representing and analyzing complex data. Recent developments have seen the introduction of novel graph neural network architectures, such as Functional Connectivity Graph Neural Networks and Hypergraph Neural Networks, which have shown significant performance gains over existing methods. Additionally, topological methods, such as those using persistent graph homology and digital homology, have been applied to various domains, including physics, biometrics, and materials science, demonstrating their potential for providing compact, interpretable, and accurate representations of complex data. Noteworthy papers in this area include: A Graph Neural Network Approach for Mapping the Conceptual Structure and Inter-Branch Connectivity of Physics, which introduces a novel framework for representing physical laws as a weighted knowledge graph. Implicit Hypergraph Neural Networks, which brings the implicit equilibrium formulation to hypergraphs, enabling stable and efficient global propagation across hyperedges without deep architectures. Topological Invariant-Based Iris Identification via Digital Homology and Machine Learning, which presents a biometric identification method based on topological invariants from 2D iris images, offering a compact, interpretable, and accurate alternative to deep learning.