High-order Knowledge Based Network Controllability Robustness Prediction: A Hypergraph Neural Network Approach

TL;DR

A dual hypergraph attention neural network model based on high-order knowledge (NCR-HoK) is proposed to accomplish the tasks of robustness learning and controllability robustness curve prediction and explores for the first time the impact of high-order knowledge on the network's controllable robustness.

Abstract

In order to evaluate the invulnerability of networks against various types of attacks and provide guidance for potential performance enhancement as well as controllability maintenance, network controllability robustness (NCR) has attracted increasing attention in recent years. Traditionally, controllability robustness is determined by attack simulations, which are computationally time-consuming and only applicable to small-scale networks. Although some machine learning-based methods for predicting network controllability robustness have been proposed, they mainly focus on pairwise interactions in complex networks, and the underlying relationships between high-order structural information and controllability robustness have not been explored. In this paper, a dual hypergraph attention neural network model based on high-order knowledge (NCR-HoK) is proposed to accomplish robustness learning and controllability robustness curve prediction. Through a node feature encoder, hypergraph construction with high-order relations, and a dedicated dual hypergraph attention module, the proposed method can effectively learn three types of network information simultaneously: explicit structural information in the original graph, high-order connection information in local neighborhoods, and hidden features in the embedding space. Notably, we explore for the first time the impact of high-order knowledge on network controllability robustness. Compared with state-of-the-art methods for network robustness learning, the proposed method achieves superior performance on both synthetic and real-world networks with low computational overhead.

Figures (11)

• Figure 1: The Overview of the proposed NCR-HoK framework. NCR-HoK can effectively learn three types of network information simultaneously: the explicit structural information in the original graph, the high-order connection information in local neighborhoods and more hidden structures and features in the embedding space.
• Figure 2: The Principle of Hypergraph Generation by K-Hop and K-NN.
• Figure 3: The predictions of the controllable robustness curves for different network types under the RAs condition by NCR-HoK, PCR, and iPCR models. $P_N$ represents the number of nodes having been removed from the network; and $n_D$ is calculated by \ref{['1']}. RA (x)-$\textless{}k\textgreater{}$=(y) represents the true values of the controllable robustness curve under the RA condition for a network of type (x) with an average degree of (y), as well as the prediction results of each model.
• Figure 4: The predictions of the controllable robustness curves for different types of network under the RA condition by NCR-HoK, PCR27, iPCR28 and CRL-SGNNCRL-SGNN models. $P_N$ represents the number of nodes having been removed from the network; and $n_D$ is calculated by \ref{['1']}. RA (x)-$<k>$=(y) represents the true values of the controllable robustness curve under the RA condition for a network of type (x) with an average degree of (y), as well as the prediction results of each model.
• Figure 5: The predictions of the controllable robustness curves for various types of network with different node sizes under the RAs condition by the NCR-HoK, PCR27, iPCR28 and CRL-SGNNCRL-SGNN models.