  General graphs are difficult for learning due to their irregular structures.
Existing works employ message passing along graph edges to extract local
patterns using customized graph kernels, but few of them are effective for the
integration of such local patterns into global features. In contrast, in this
paper we study the methods to transfer the graphs into trees so that explicit
orders are learned to direct the feature integration from local to global. To
this end, we apply the breadth first search (BFS) to construct trees from the
graphs, which adds direction to the graph edges from the center node to the
peripheral nodes. In addition, we proposed a novel projection scheme that
transfer the trees to image representations, which is suitable for conventional
convolution neural networks (CNNs) and recurrent neural networks (RNNs). To
best learn the patterns from the graph-tree-images, we propose TreeRNN, a 2D
RNN architecture that recurrently integrates the image pixels by rows and
columns to help classify the graph categories. We evaluate the proposed method
on several graph classification datasets, and manage to demonstrate comparable
accuracy with the state-of-the-art on MUTAG, PTC-MR and NCI1 datasets.
