Parametric Graph Representations in the Era of Foundation Models: A Survey and Position

Graphs have been widely used in the past decades of big data and AI to model comprehensive relational data. When analyzing a graph's statistical properties, graph laws serve as essential tools for parameterizing its structure. Identifying meaningful graph laws can significantly enhance the effectiveness of various applications, such as graph generation and link prediction. Facing the large-scale foundation model developments nowadays, the study of graph laws reveals new research potential, e.g., providing multi-modal information for graph neural representation learning and breaking the domain inconsistency of different graph data. In this survey, we first review the previous study of graph laws from multiple perspectives, i.e., macroscope and microscope of graphs, low-order and high-order graphs, static and dynamic graphs, different observation spaces, and newly proposed graph parameters. After we review various real-world applications benefiting from the guidance of graph laws, we conclude the paper with current challenges and future research directions.