  Graph Neural Networks (GNNs) have achieved tremendous success in various
real-world applications due to their strong ability in graph representation
learning. GNNs explore the graph structure and node features by aggregating and
transforming information within node neighborhoods. However, through
theoretical and empirical analysis, we reveal that the aggregation process of
GNNs tends to destroy node similarity in the original feature space. There are
many scenarios where node similarity plays a crucial role. Thus, it has
motivated the proposed framework SimP-GCN that can effectively and efficiently
preserve node similarity while exploiting graph structure. Specifically, to
balance information from graph structure and node features, we propose a
feature similarity preserving aggregation which adaptively integrates graph
structure and node features. Furthermore, we employ self-supervised learning to
explicitly capture the complex feature similarity and dissimilarity relations
between nodes. We validate the effectiveness of SimP-GCN on seven benchmark
datasets including three assortative and four disassorative graphs. The results
demonstrate that SimP-GCN outperforms representative baselines. Further probe
shows various advantages of the proposed framework. The implementation of
SimP-GCN is available at \url{https://github.com/ChandlerBang/SimP-GCN}.
