The study of information spreading based on the complex network theory and topological structure has become an important issue in complex networks. Plenty of infectious disease models are widely used for information diffusion research in complex networks. Based on these state-of-the-art models, a new epidemic dynamic model with dynamic evolution equations is proposed and performed on the homogeneous and heterogeneous networks, respectively, in this paper. Meanwhile, we divide the propagation states into two states: L and H (low propagation ability groups and high propagation ability groups) and consider the transformation of these two states in our model. Then, the equilibria and stability of the model are analyzed for both homogeneous and heterogeneous networks to verify the validity of the proposed model. Finally, simulation results illustrate that the proposed model and information propagation dynamic evolution equations are reasonable and effective. Experiments with effect factors also reveal the interaction mechanism and the diffusion process of the proposed model in complex networks.

Social recommendation systems can improve recommendation quality in cases of sparse user–item interaction data, which has attracted the industry’s attention. In reality, social recommendation systems mostly mine real user preferences from social networks. However, trust relationships in social networks are complex and it is difficult to extract valuable user preference information, which worsens recommendation performance. To address this problem, this paper proposes a social recommendation algorithm based on multi-graph contrastive learning. To ensure the reliability of user preferences, the algorithm builds multiple enhanced user relationship views of the user’s social network and encodes multi-view high-order relationship learning node representations using graph and hypergraph convolutional networks. Considering the effect of the long-tail phenomenon, graph-augmentation-free self-supervised learning is used as an auxiliary task to contrastively enhance node representations by adding uniform noise to each layer of encoder embeddings. Three open datasets were used to evaluate the algorithm, and it was compared to well-known recommendation systems. The experimental studies demonstrated the superiority of the algorithm.

Using attribute graphs for node embedding to detect community structure has become a popular research topic. However, most of the existing algorithms mainly focus on the network structure and node features, which ignore the higher-order relationships between nodes. In addition, only adopting the original graph structure will suffer from sparsity problems, and will also result in sub-optimal node clustering performance. In this paper, we propose a hypergraph network embedding (HGNE) for community detection to solve the above problems. Firstly, we construct potential connections based on the shared feature information of the nodes. By fusing the original topology with feature-based potential connections, both the explicit and implicit relationships are encoded into the node representations, thus alleviating the sparsity problem. Secondly, for integrating the higher-order relationship, we adopt hypergraph convolution to encode the higher-order correlations. To constrain the quality of the node embedding, the spectral hypergraph embedding loss is utilized. Furthermore, we design a dual-contrast mechanism, which draws similar nodes closer by comparing the representations of different views. This mechanism can efficiently prevent multi-node classes from distorting less-node classes. Finally, the dual-contrast mechanism is jointly optimized with self-training clustering to obtain more robust node representations, thus improving the clustering results. Extensive experiments on five datasets indicate the superiority and effectiveness of HGNE.