Abstarct: Abstract Many information retrieval (IR) systems experience significant fluctuations in performance in response to user queries. Even for systems that generally perform well on average, the quality of query results can be low for certain requests. Therefore, it is important for IR systems to be able to identify "difficult" queries so that they can respond to them appropriately. Understanding the inherent reasons for the difficulty of some queries compared to others is essential for advancing the field of IR, and providing an appropriate response to this important question could help search engines reduce performance variability and thus better meet their customers' needs. The task of query performance prediction (QPP) is described as estimating retrieval effectiveness in the absence of relevance judgments, and estimating query difficulty is an attempt to quantify the quality of search results obtained for a specific query from a defined set of retrieved documents. Thus, our goal in this research is to predict query performance using graph metrics. These metrics are calculated on a graph where the nodes represent the retrieved documents and the edges indicate similarities between these documents. The calculation of document similarity through graph modeling is performed using the new technique, Sentence-BERT, along with the older and widely used technique, Word2Vec. Additionally, experiments have been conducted to examine the dependence of actual query performance and the estimated query difficulty baxsed on Pearson, Spearman, and Kendall correlation coefficients, with these experiments carried out on the MSMARCO dataset.