This paper proposes a novel approach to represent the geometry of the corrugated board profile during compression by using graphs. Graphs are lighter than images, and the computational time of compression analysis is then significantly reduced compared to using the original image data for the same analysis. The main goal of using such graphs is to gain more knowledge about the mechanical behavior of corrugated boards under compression compared to the current load-deformation curve approach. A node-tracking algorithm is applied to characterize the different phases happening during the compression test in order to predict physical phenomena, including buckling and contact. The main results show that analyzing the nodes provides significant insights into the compression phases, which was not achieved in the current state-of-the-art. The authors believe the object of this research is crucial to better understand the physics of corrugated boards under compression, and it can also be extended to other engineering structures.