A More Motivating Examples and Analysis

Additional explanations for Table 1 We provide two real examples of how graph properties can decide important graph patterns as the signals for graph classifications. The first example is about social networks. This may be an important signal for effective graph classification, which is consistent with commonly used social network classification methods such as motif-counting. On the other hand, if a set of random graphs does not possess high CC, the prominent graph patterns might be some subtrees or long edges, where the training of a graph classification model is not likely to facilitate the capturing of triangles, and thus not beneficial for the classification of social networks. Although the two datasets are from totally different domains, they are both formed by spatial structures, which is reflected in Table 1 where the two datasets have very close values regarding multiple properties (degree distribution, shortest path length, CC).