This study proposes a formal model to determine user influence on social media, applying directed and weighted graphs and addressing the challenge of measuring influence through indirect interaction metrics. We contribute two directed and weighted graph models creatively designed to represent user-post-user interactions and user-user relationships based on mentions. These models allow for a practical analysis of complex interactions in social networks. The influence score combines four key factors: centrality, reach, content creation, and content reception. Experiments on two datasets from the X social media platform–focusing on user-mention relationships–show that the model achieves a Spearman correlation of around 97% and ranks quality above 85% when content-related factors are prioritized. The results highlight the important role of content quality and sentiment in evaluating user influence. This method provides a strong framework for analyzing the influence of social networks, with potential applications in marketing, media, and especially fake news detection. Research opens up new directions for exploring types of influence and social relationships, particularly by integrating emotional expressions to assess engagement levels.