Identification of key spreaders in complex network by integrating dynamic characteristics and local structure of nodes

Identifying the most influential nodes in the spreading process in complex networks is crucial in many applications, such as accelerating the diffusion of information and suppressing the spread of viruses or rumors. Existing methods of identifying influential spreaders have their limitations. Specifically speaking, classical network centrality methods rely solely on local or global topology to predict node influence; traditional machine learning and deep learning methods are not suitable for graph-structured data; existing graph neural network-based methods neglect the dynamic characteristics of the propagation process itself. Researchers have pointed out that the spreading influence of nodes not only depends on their structural location, but is also significantly influenced by the dynamics of the spreading process itself. In this work, we propose a propagation dynamics graph neural network (PDGNN) that integrates the dynamic features of the propagation process and the structural features of nodes to identify influential nodes. Specifically speaking, based on the susceptible-infected-recovered (SIR) propagation model, the dynamic infection features and potential infection capacity of nodes are extracted from the epidemic spreading process. Then a high-dimensional feature vector of each node consisting of the embedding and degree of its local transmission tree, as well as its dynamics-sensitive centrality is constructed and used as the input to the graph neural network. To deal with the problem of imbalanced numbers between critical nodes and non-critical nodes in training the model and optimizing the output, an optimized loss function is designed, which combines focal loss with mean squared error. Experimental results in two synthetic networks and seven real-world networks show that the PDGNN outperforms classical centrality methods, traditional machine learning and deep learning-based methods, and existing graph neural network-based methods in identifying influential nodes in the spreading process in complex networks. The performance of PDGNN is robust when the infection rate and the size of the training set change. In a wide range of infection rates, the proposed PDGNN can accurately identify influential spreaders. Despite the fact that the training set accounts for 30% of the total dataset, the PDGNN has the smallest inaccuracy in all nine studied networks.