  Autonomous individuals establish a structural complex system through pairwise
connections and interactions. Notably, the evolution reflects the dynamic
nature of each complex system since it recodes a series of temporal changes
from the past, the present into the future. Different systems follow distinct
evolutionary trajectories, which can serve as distinguishing traits for system
classification. However, modeling a complex system's evolution is challenging
for the graph model because the graph is typically a snapshot of the static
status of a system, and thereby hard to manifest the long-term evolutionary
traits of a system entirely. To address this challenge, we suggest utilizing a
heat-driven method to generate temporal graph augmentation. This approach
incorporates the physics-based heat kernel and DropNode technique to transform
each static graph into a sequence of temporal ones. This approach effectively
describes the evolutional behaviours of the system, including the retention or
disappearance of elements at each time point based on the distributed heat on
each node. Additionally, we propose a dynamic time-wrapping distance GDTW to
quantitatively measure the distance between pairwise evolutionary systems
through optimal matching. The resulting approach, called the Evolution Kernel
method, has been successfully applied to classification problems in real-world
structural graph datasets. The results yield significant improvements in
supervised classification accuracy over a series of baseline methods.
