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Abstract The influence maximization problem that has drawn a great deal of attention from researchers aims to identify a subset of influential spreaders that can maximize the expected influence spread in social networks. Existing works on the problem primarily concentrate on developing non-adaptive policies, where all seeds will be ignited at the very beginning of the diffusion after the identification. However, in non-adaptive policies, budget redundancy could occur as a result of some seeds being naturally infected by other active seeds during the diffusion process. In this paper, the adaptive seeding policies are investigated for the intractable adaptive influence maximization problem. Based on deep learning model, a novel approach named graph convolutional networks with self-attention mechanism (ATGCN) is proposed to address the adaptive influence maximization as a regression task. A controlling parameter is introduced for the adaptive seeding model to make a tradeoff between the spreading delay and influence coverage. The proposed approach leverages the self-attention mechanism to dynamically assign importance weight to node representations efficiently to capture the node influence feature information relevant to the adaptive influence maximization problem. Finally, intensive experimental findings on six real-world social networks demonstrate the superiorities of the adaptive seeding policy over the state-of-the-art baseline methods to the conventional influence maximization problem. Meanwhile, the proposed adaptive seeding policy ATGCN improves the influence spread rate by up to 7% in comparison to the existing state-of-the-art greedy-based adaptive seeding policy.

Exploring effective and efficient strategies for identifying influential nodes from social networks as seeds to promote the propagation of influence remains a crucial challenge in the field of influence maximization (IM), which has attracted significant research efforts. Deep learning-based approaches have been adopted as an alternative promising solution to the IM problem. However, a robust model that captures the associations between network information and node influence needs to be investigated, while concurrently considering the effects of the overlapped influence on training labels. To address these challenges, a GCNT model, which integrates Graph Convolutional Networks with Graph Transformers, is introduced in this paper to capture the intricate relationships among the topology of the network, node attributes, and node influence effectively. Furthermore, an innovative method called Greedy-LIE is proposed to generate labels to alleviate the issue of overlapped influence spread. Moreover, a Mask mechanism specially tailored for the IM problem is presented along with an input embedding balancing strategy. The effectiveness of the GCNT model is demonstrated through comprehensive experiments conducted on six real-world networks, and the model shows its competitive performance in terms of both influence maximization and computational efficiency over state-of-the-art methods.