The development of artificial intelligence has led to a dramatic leap in large language models (LLMs), which understand and generate various kinds of unstructured data such as text, images, and speech. Today, LLMs have gone beyond sentence generation to the point of writing code, reviewing legal documents, and solving logical puzzles.

Meanwhile, many problems in the real world consist of entities and the complex multidimensional relationships between them. Social networks that deal with interactions between people, the complex supply chain structures of global companies, the spread paths of infectious diseases, and even biological protein structures or urban traffic road networks — this vast amount of information is mathematically represented as a non-sequential and topological structure called a “graph.”

So then, we can ask the question: “Can a Transformer-based LLM, which is specialized in reading and writing text sequentially, perform complex graph operations such as social network analysis (SNA) on its own?”

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First, let me state the conclusion.

Current LLMs are excellent at extracting graph structures from qualitative unstructured text and explaining them semantically,

but they show limitations
when trying to calculate the topological structure of a graph in their “heads,”
such as finding the shortest path or mathematically separating complex communities.

In other words, LLMs are very strong at language-based explanation and interpretation, but they cannot yet fully replace the full-scale graph computations required in social network analysis.

Recent studies have specifically analyzed which parts of graph-operation tasks LLMs are strong at and where they show limitations.

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