TECNN: Identification of key nodes in complex networks based on transformer encoder and Convolutional Neural Network

Abstract

In complex networks, identifying key nodes is crucial for controlling information dissemination, optimizing resource allocation, and enhancing network robustness. Although many methods for identifying key nodes have been proposed, most deep learning-based approaches lack in-depth study of multi-hop neighbor relationships when constructing node features, often ignoring critical information and thus affecting identification accuracy. To address this issue, we propose a hybrid model based on the Transformer encoder and Convolutional Neural Network (TECNN) to better capture comprehensive information of nodes and predict their diffusion influence. Firstly, we use the neighborhood aggregation module to aggregate the 7-hop neighbor features of the nodes, obtaining a neighborhood matrix for the nodes. Next, the neighborhood matrix is fed into the Transformer encoder to capture the long-range dependencies between nodes, producing new node feature representations. These new node representations are then input into the Convolutional Neural Network, and the structural information of the nodes is further extracted through multilayer convolutional operations. Finally, a fully connected layer is used to predict the influence of the nodes. We perform comparative experiments by comparing the TECNN algorithm with four classical centrality algorithms and three state-of-the-art deep learning-based algorithms on 12 networks. The experimental results show that TECNN performs well in terms of ranking accuracy, discriminative ability, and top-10 node identification precision.