The rapid spread of misinformation and rumors on social media platforms, particularly Twitter, poses significant risks to public perception and decision-making. This study presents a comprehensive approach to analyzing and mitigating rumor propagation by identifying key influencers and optimizing propagation time within online communities. Our dataset consists of over 800,000 nodes with interactions categorized as retweets, mentions, and replies, each assigned an influence score to quantify user impact. Using the Infomap algorithm, we initially detected 13,500 communities and filtered them to retain 67 influential clusters with a higher number of nodes and stronger influence scores. To analyze the spread of rumors, we developed an algorithm that tracks propagation within these communities, leveraging top influencers as initial spreaders and computing the average propagation time. Furthermore, we introduced a node deletion strategy to iteratively remove high-impact influencers, reducing the overall propagation time and limiting misinformation spread. Finally, we adjusted the propagation times by normalizing them with the earliest influencer timestamps to ensure precise measurement. Our findings highlight that targeted removal of key spreaders significantly disrupts rumor diffusion, providing insights into optimizing influence-based network interventions for misinformation control.