The recent advancements in graph data analysis have significantly focused on enhancing the scalability and efficiency of graph embedding techniques. Researchers are increasingly leveraging lower-dimensional representations to simplify the analysis of large-scale graphs, enabling dynamic updates and facilitating experimentation with various embedding methods. Notably, there is a growing emphasis on preserving community structures within these embeddings, which is crucial for understanding the mesoscopic organization of networks. Novel algorithms, such as the Two Layer Walk, have demonstrated superior performance in tasks like link prediction by balancing intra- and inter-community relationships without additional computational overhead. Additionally, the study of temporal networks has introduced innovative approaches to clustering time-snapshots, allowing for the detection of significant structural shifts over time. These methods, validated through synthetic and real-world datasets, offer insights into the dynamics of complex systems. Furthermore, the exploration of spatial networks has highlighted the vulnerability of connectivity caused by local communities, particularly in the context of urban planning and infrastructure. Lastly, the use of app usage data to unveil social vibrancy in urban spaces has provided a novel computational approach to understanding sociospatial behaviors and their impact on urban environments. These developments collectively push the boundaries of graph analysis, temporal network modeling, and urban studies, offering new tools and insights for professionals in these fields.