Analysis of the Effect of Social Circles on the Grade Point Average of Mathematics Students in the Class Of 2025 Using a Graph Theory Approach

Alfian Putra Ardana; Rodiyatul Adawiyah; I Gede Adhitya Wisnu Wardhana; Rohaidah Masri; Maris Tabalon Lasco; Deni Hamdani

doi:10.31764/jtam.v10i4.40648

Analysis of the Effect of Social Circles on the Grade Point Average of Mathematics Students in the Class Of 2025 Using a Graph Theory Approach

Alfian Putra Ardana, Rodiyatul Adawiyah, I Gede Adhitya Wisnu Wardhana, Rohaidah Masri, Maris Tabalon Lasco, Deni Hamdani

Abstract

Student academic achievement, as measured by Grade Point Average (GPA), is influenced by various factors, including the social environment. This study aims to analyze the relationship between friendship networks and students' GPA using a graph theory approach, offering an alternative perspective to conventional perception-based analyses of peer influence. The study involved 93 students from the Mathematics Study Program at the University of Mataram. Friendship data were collected through a structured sociometric questionnaire administered via Google Forms, while GPA data were obtained from the official academic records of the study program with formal authorization. Students were represented as vertices and friendship relationships as weighted edges based on the level of closeness. The friendship network was analyzed using graph theory, and the relationship between node degree and GPA was examined through simple linear regression. The results revealed a weak and statistically insignificant relationship between friendship networks and students' GPA. These findings suggest that the structural characteristics of friendship networks alone are insufficient to explain academic performance, which is likely influenced by multiple academic and social factors. This study demonstrates the potential of graph theory as an alternative approach for modeling friendship networks and provides a foundation for future research incorporating more comprehensive network metrics and additional explanatory variables.

Keywords

Graph Theory; Node Degree; Friendship; GPA; Linear Regression.

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DOI: https://doi.org/10.31764/jtam.v10i4.40648