Over-smoothing is a persistent challenge in Graph Neural Networks (GNNs), where node embeddings become indistinguishable as network depth increases, fundamentally limiting their effectiveness on tasks requiring fine-grained distinctions. This issue arises from the reliance on diffusion-based propagation mechanisms, which suppress high-frequency information essential for preserving feature diversity. To mitigate this, we propose a wave-driven GNN framework that redefines feature propagation through the wave equation. Unlike diffusion, the wave equation incorporates second-order dynamics, balancing smoothing with oscillatory behavior to retain high-frequency components while ensuring effective information flow. To enhance the stability and convergence of wave equation discretization on graphs, an energy-based mechanism inspired by kinetic and potential energy dynamics is introduced, balancing temporal evolution and structural alignment to stabilize propagation. Extensive experiments on benchmark datasets, including Cora, Citeseer, and PubMed, as well as real-world graphs, demonstrate that the proposed framework achieves state-of-the-art performance, effectively mitigating over-smoothing and enabling deeper, more expressive architectures. The code is available at https://github.com/rene0329/EWGNN/.

Social relationships offer crucial supplementary information for recommendations by leveraging users' social connections to gain insights into their preferences. However, prevalent social recommendation methods often grapple with the issues of sparsity and noise, which curtail their effectiveness. In addition, these methods overlook the intricacies of user interactions within social networks, which could provide invaluable information. Addressing their deficiencies, this article introduces a novel sociological-theory-based multitopic self-supervised recommendation method (SMSR). This method integrates user attitude information into the construction of social relationships and utilizes dynamic routing to identify and categorize topics, thereby mitigating the impact of social noise on recommendation accuracy. Furthermore, we reveal sophisticated higher order user relations within these topics by using motifs. By combining the light graph convolutional network with balance theory, SMSR efficiently aggregates information from diverse social relations to gain its outstanding performance. Moreover, we have devised and integrated four self-supervised signals, inspired by social theory and derived from heterogeneous graph analysis, to more effectively exploit the rich structural and semantic information inherent in social relationship graphs. Empirical results from extensive experiments on publicly available datasets underscore SMSR's superiority over the state of the art.

Air pollution has caused a bad effect on the natural environment and public health. With the rapid establishment of air monitoring stations and meteorological stations, the volume of air pollution data is increasing dramatically. The traditional methods to model the air pollution transmission process have shown a limitation to process a large amount of non-linear data. Machine learning methods have recently been proven to be extremely efficient and accurate to process data in complex structures. In this paper, a novel method based on a complex network is proposed to discover the air monitoring station communities and analyze the air pollutants diffusion. The method comprises several aspects, including a dimension reduction process, a complex network generation process, and a community detection process. The proposed method was verified based on a real-world air pollution dataset, and the results demonstrate that the air pollutants diffusion has a community structure, and some critical air monitoring stations have a greater influence on the transmission of pollutants, which should be paid more attention to the following air quality management.