Empowering Interdisciplinary Insights with Dynamic Graph Embedding Trajectories

Background Dynamic graphs (DGs) are ubiquitous data structures present in various realworld evolving systems, such as social networks [1], linguistics [2], international relations [3], and computational finance [4]. Representing these dynamic graphs efficiently has become a crucial challenge due to their massive sizes and ever-changing nature. One compelling approach to tackle this challenge is discrete-time dynamic graph (DTDG) models [5-7], which represent a dynamic graph as a series of snapshots, each containing the nodes and edges that co-occur at particular timestamps. Despite the effectiveness of DTDG models in a wide range of graph-oriented tasks such as link prediction, node classification, and edge regression, these models usually remain opaque to researchers in terms of interpretability. The high-dimensional representations generated by these models make it difficult for users to extract and understand the intrinsic value from dynamic graphs. Currently, researchers often manually analyze the dynamic graph data, as there are no specialized tools to support this process [8, 9]. However, manual analysis of enormous dynamic graphs covering multiple timestamps can be overwhelming, and the continuously evolving nature of these graphs makes it challenging to intuitively capture both micro-level and macro-level structural shifts. For instance, in the study of international relations, aside from predicting graph attributes like future bilateral trade volumes, it is vital to understand microlevel changes such as a country's alliance network, trade relations, and conflict dynamics, as 1