  Convolution and pooling are the key operations to learn hierarchical
representation for graph classification, where more expressive $k$-order($k>1$)
method requires more computation cost, limiting the further applications. In
this paper, we investigate the strategy of selecting $k$ via neighborhood
information gain and propose light $k$-order convolution and pooling requiring
fewer parameters while improving the performance. Comprehensive and fair
experiments through six graph classification benchmarks show: 1) the
performance improvement is consistent to the $k$-order information gain. 2) the
proposed convolution requires fewer parameters while providing competitive
results. 3) the proposed pooling outperforms SOTA algorithms in terms of
efficiency and performance.
