Graph theory allows the student to work on problems that require imagination, intuition, systematic exploration, conjecturing, and reasoning. It implies that mathematical investigation skill is essential to be proficient in Graph Theory. In this study, we conduct empirical research that deals with associational research. There were 97 students selected purposively from sophomore students in the Discrete Mathematics course offered by one of the mathematics education departments in Indonesia. The empirical evidence was analyzed to explain students' thinking behavior on Graph Theory by discovering the association structure between prior knowledge and mathematical investigation skill, then visually depicting its association using the k-means clustering procedure and correspondence analysis. Since in our department, we expect certain prior skills, then this visualization could be used as self-reflection for our department, whether we have gained the results as expected to strengthen certain investigation approaches. Generally, the study concludes some findings that provide novelty and open issues for future research to develop a learning environment supporting mathematical investigation activities.