This research is motivated by the lack of understanding of students toward the use of circular matrix in finding their concepts. The purpose of this study is to find out the practicality of using the Circular Matrix to Determine the Spectrum of Circle Graphs and Inquiry-Based Cubic Graphs in Mathematics Education Students of Medan State University. This type of research is development research with the IDI Model (Instructional Development Institute) which applies the principles of a systematic approach consisting of 3 major stages, namely determination or analysis of needs, development, and evaluation. At this stage, it is discussed the practicality of the use of an inquiry-based circular matrix. The instrument used is a written interview with students and spread practicality questionnaires. Based on the results of the interview obtained information, students more easily understand the material, because it guides fellow students in finding concepts when working on examples of problems given by lecturers. Based on the results of the analysis of student questionnaires obtained a level of 86.7% (very practical). The graph spectrum is a collection of different eigenvalues and their multiplicity. Determining the graph spectrum can be done in several ways, including using a circular matrix. Circular matrix is widely applied in various areas of life, including analyzing vibrations in differential equations, determining the spectrum of a graph, and others. In this paper, the spectrum of circle graphs and cubic graphs is determined using a circular matrix. The results of the study were obtained:

Graph spectrum, Circular matrix, eigen value, multiplicity