<![CDATA[Discussion-based learning methods are approaches often used by teachers to encourage students to share views, skills, and knowledge. Lack of student engagement, uneven interaction, difficulty identifying interaction patterns and lack of data-based strategies to improve interaction are problems in discussion-based learning methods. Graph theory can be shown its role and usefulness in solving various problems by studying and analyzing models or formulas. The purpose of this study is to analyze the application of graph theory and discussion learning methods to improve interaction between students in the mathematics learning process in the classroom. This study was conducted at SMP Negeri 27 Medan and was conducted using qualitative methods. The results showed that the application of directed graph theory was able to improve interaction between students in learning discussions. Of the five groups formed, three groups showed good interaction dynamics through effective role sharing and active communication, while the other two groups were less successful due to lack of coordination and leadership. The directed graph pattern makes it easier to identify communication patterns, so it can be a guide for teachers in structuring groups that are more inclusive and effective. The implications of this research suggest that graph theory can help create collaborative learning environments and support overall student success.]]>
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