Graphs and Artificial Intelligence.

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“Graph theory reveals the hidden blueprint of data, while AI builds the edifice of understanding.”

Graphs — mathematical structures consisting of nodes and edges — provide a natural way to represent relationships. Their utility spans from analyzing social networks to modeling molecular structures. As AI systems strive to understand and learn from relational data, graphs have emerged as a crucial tool. Today, methods like Graph Neural Networks (GNNs) extend conventional deep learning, enabling models to process irregular, non-Euclidean data. In this report, we recount the evolution of graph-based approaches in AI, discuss landmark research, and propose new directions for exploration.

Historical Perspective

The origins of graph theory date back to 1736, when Leonhard Euler solved the famous Königsberg bridge problem. This early work laid the mathematical foundation for studying networks and complex relationships. Over the centuries, graphs evolved from a purely theoretical construct into a versatile tool for representing interconnected systems in diverse fields. As computational methods advanced, researchers recognized that many problems in artificial intelligence — from semantic networks to recommendation systems — could benefit from graph-based…