Social media platforms have revolutionized information exchange and socialization in today's world. Twitter, as one of the prominent platforms, enables users to connect with others and express their opinions. This study focuses on analyzing user engagement levels on Twitter using graph mining and clustering techniques. We measure user engagement based on various tweet attributes, including retweets, replies, and more. Specifically, we explore the strength of user connections in Twitter networks by examining the diversity of edges. Our approach incorporates graph mining models that assign different weights to evaluate the significance of each connection. Additionally, clustering techniques are employed to group users based on their engagement patterns and behaviors. Statistical analysis was conducted to assess the similarity between user profiles, as well as attributes, such as friendship, followings, and interactions within the Twitter social network. The findings highlight the discovery of closely linked user groups and the identification of distinct clusters based on engagement levels. This research emphasizes the importance of understanding both individual and group behaviors in comprehending user engagement dynamics on Twitter. [ABSTRACT FROM AUTHOR]