A Graph-Neural-Network-Entropy model of vital node identification on network attack and propagation

Vital nodes usually play a key role in complex networks. Uncovering these nodes is an important task in protecting the network, especially when the network suffers intentional attack. Many existing methods have not fully integrated the node feature, interaction and state. In this article, we propose a novel method (GNNE) based on graph neural networks and information entropy. The method employs a Graph Convolutional Network (GCN) to learn the nodes' features, which are input into a Graph Attention Network (GAT) to obtain the influence factor of nodes, and the node influence factors are used to calculate the nodes' entropy to evaluate the node importance. The GNNE takes advantage of the GCN and GAT, with the GCN well extracting the nodes' features and the GAT aggregating the features of the nodes' neighbors by using the attention mechanism to assign different weights to the neighbors with different importance, and the nodes' entropy quantifies the nodes' state in the network. The proposed method is trained on a synthetic Barabasi-Albert network, and tested on six real datasets. Compared with eight traditional topology-based methods and four graph-machine-learning-based methods, the GNNE shows an advantage for the vital node identification in the perspectives of network attack and propagation.