A graph convolutional network model based on regular equivalence for identifying influential nodes in complex networks

The identification of influential nodes in complex networks is an interesting problem. Traditional approaches, such as metric- and machine learning-based approaches, often fail to adequately consider the network structure or node features, limiting their applications in certain scenarios. Deep learning-based methods, particularly those using graph neural networks (GNNs), have yielded remarkable results in this field. However, there is a lack of utilization of the regular equivalence-based similarity between nodes to feature construction, which is critical to deep learning-based methods. Nevertheless, regular equivalence-based similarity is extremely suitable to the quantification of the similarity between influential nodes, as these nodes usually have similar structural properties but do not require common neighbors. Building upon graph convolutional network (GCN, a specific type of GNN) and the regular equivalence-based similarity, this study proposes a novel method for identifying influential nodes in complex networks. Particularly, the regular equivalence-based similarities between nodes are considered to construct node features; a GCN is enhanced to improve the identification of influential nodes. Experiments on several datasets indicate that the proposed method is superior to stateof-the-art methods, demonstrating the advantages of the proposed feature construction based on regular equivalence-based similarity over the identification of influential nodes.