Exploring network reliability by predicting link status based on simplex neural network

Abstract

Complex networks are graph-based structures with non-trivial topological features that frequently occur in real systems. Link prediction plays an important role in various real-world networks application, such as recommendation systems, protein structure prediction, packet forwarding strategy optimization, etc. The existing link prediction approaches mainly focus on superficial heuristic features, while ignoring high-order structure information. In this paper, we propose a deep-learning based model, named Weisfeiler–Lehman Simplex Neural Network (WL-SNN), which can learn the high-order simplex information of the network. In particular, we design a third-order Laplace operator to extract the simplicial features and utilize the graph convolutional network to compensate for the possible deficiencies of the model resulting from the single-channel features. Furthermore, we use the Weisfeiler–Lehman algorithm to extract closed subgraphs of the target, which significantly enhances the adaptability of the model to large-scale networks. Experimental results on six real-world networks show that our approach achieves comparable performance in the link prediction task as well as in the stability analysis of the network.