Graph classification by converting static graphs into dynamic evolutionary sequences

Graphs are widely used in various fields, including industry, bioinformatics, and social systems. In these systems, individuals create a structured graph through various connections and interactions as information propagates and changes. However, most machine learning approaches represent these systems using static graphs, which pose challenges in modeling the system's evolution, as each static graph captures only a snapshot of the system's current state and often fails to reflect the evolutionary features determined by graph geometry. To address this challenge, this work proposes a Heat Kernel based Graph Evolution method. This approach converts each static graph into a sequence representing its evolutionary trajectory and classifies graphs by optimal pairwise sequence matching. This work discriminates graphs by recognizing their evolving characteristics from the perspectives of heat diffusion. Furthermore, the effectiveness of this method is demonstrated through classification tasks involving real-world molecular and social network graph datasets. The results indicate a significant improvement in accuracy of 0.3–31.8 % compared to baseline methods.