Markov clustering regularized multi-hop graph neural network

Graph Neural Networks (GNNs) have shown great potential for graph data analysis. In this paper, we focus on multi-hop graph neural networks and aim to extend existing models to a high-order multi-hop form for graph-level representation learning. However, such a directly extending method suffers from two limitations, i.e., computational inefficiency and limited representation ability of the multi-hop neighbor. For the former limitation, we utilize an iteration approach to approximate the power of a complex adjacency matrix to achieve linear computational complexity. For the latter limitation, we introduce the Regularized Markov Clustering (R-MCL) to regularize the flow matrix, i.e., the adjacency matrix, in each iteration step. With these two strategies, we construct Markov Clustering Regularized Multi-hop Graph Neural Network (MCMGN) for graph-level representation learning tasks. Specifically, MCMGN consists of a multi-hop message passing phase and a readout phase, where the multi-hop message passing phase aims to learn multi-hop node embedding, and then the readout phase aggregates multi-hop node representations to generate graph embedding for graph-level representation learning tasks. Extensive experiments on eight graph benchmark datasets strongly demonstrate the effectiveness of Markov Clustering Regularized Multi-hop Graph Neural Network, leading to superior performance on graph classification.