In recent years, Large Language Models (LLMs) gain considerable attention for their potential to enhance personalized experiences in virtual assistants and chatbots. A key area of interest is the integration of personas into LLMs to improve dialogue naturalness and user engagement. This study addresses the challenge of persona classification, a crucial component in dialogue understanding, by proposing a framework that combines text embeddings with Graph Neural Networks (GNNs) for effective persona classification. Given the absence of dedicated persona classification datasets, we create a manually annotated dataset to facilitate model training and evaluation. Our method involves extracting semantic features from persona statements using text embeddings and constructing a graph where nodes represent personas and edges capture their similarities. The GNN component uses this graph structure to propagate relevant information, thereby improving classification performance. Experimental results show that our approach, in particular the integration of GNNs, significantly improves classification performance, especially with limited data. Our contributions include the development of a persona classification framework and the creation of a dataset.