  Identifying critical nodes in networks is a classical decision-making task,
and many methods struggle to strike a balance between adaptability and utility.
Therefore, we propose an approach that empowers Evolutionary Algorithm (EA)
with Large Language Models (LLMs), to generate a function called "score\_nodes"
which can further be used to identify crucial nodes based on their assigned
scores. Our model consists of three main components: Manual Initialization,
Population Management, and LLMs-based Evolution. It evolves from initial
populations with a set of designed node scoring functions created manually.
LLMs leverage their strong contextual understanding and rich programming skills
to perform crossover and mutation operations on the individuals, generating
excellent new functions. These functions are then categorized, ranked, and
eliminated to ensure the stable development of the populations while preserving
diversity. Extensive experiments demonstrate the excellent performance of our
method, showcasing its strong generalization ability compared to other
state-of-the-art algorithms. It can consistently and orderly generate diverse
and efficient node scoring functions. All source codes and models that can
reproduce all results in this work are publicly available at this link:
\url{https://anonymous.4open.science/r/LLM4CN-6520}
