In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models. Here, based on an optimization method, we investigate the feasibility of improving graph classification performance while simplifying the model learning process. Inspired by progress in structural information assessment, we optimize the given data sample from graphs to encoding trees. In particular, we minimize the structural entropy of the transformed encoding tree to decode the key structure underlying a graph. This transformation is denoted as structural optimization. Furthermore, we propose a novel feature combination scheme, termed hierarchical reporting, for encoding trees. In this scheme, features are transferred from leaf nodes to root nodes by following the hierarchical structures of encoding trees. We then present an implementation of the scheme in a tree kernel and a convolutional network to perform graph classification. The tree kernel follows label propagation in the Weisfeiler-Lehman (WL) subtree kernel, but it has a lower runtime complexity $O(n)$. The convolutional network is a special implementation of our tree kernel in the deep learning field and is called Encoding Tree Learning (ETL). We empirically validate our tree kernel and convolutional network with several graph classification benchmarks and demonstrate that our methods achieve better performance and lower computational consumption than competing approaches.