A Learning Convolutional Neural Network Approach for Network Robustness Prediction

Network Robustness Prediction: Influence of Training Data Distributions

Network robustness refers to the ability of a network to continue its functioning against malicious attacks, which is critical for various natural and industrial networks. Network robustness can be quantitatively measured by a sequence of values that record the remaining functionality after a sequential node- or edge-removal attacks. Robustness evaluations are traditionally determined by attack simulations, which are computationally very time-consuming and sometimes practically infeasible. The convolutional neural network (CNN)-based prediction provides a cost-efficient approach to fast evaluating the network robustness. In this article, the prediction performances of the learning feature representation-based CNN (LFR-CNN) and PATCHY-SAN methods are compared through extensively empirical experiments. Specifically, three distributions of network size in the training data are investigated, including the uniform, Gaussian, and extra distributions. The relationship between the CNN input size and the dimension of the evaluated network is studied. Extensive experimental results reveal that compared to the training data of uniform distribution, the Gaussian and extra distributions can significantly improve both the prediction performance and the generalizability, for both LFR-CNN and PATCHY-SAN, and for various functionality robustness. The extension ability of LFR-CNN is significantly better than PATCHY-SAN, verified by extensive comparisons on predicting the robustness of unseen networks. In general, LFR-CNN outperforms PATCHY-SAN, and thus LFR-CNN is recommended over PATCHY-SAN. However, since both LFR-CNN and PATCHY-SAN have advantages for different scenarios, the optimal settings of the input size of CNN are recommended under different configurations.

A Critical Candidate Node-Based Attack Model of Network Controllability

The controllability of complex networks is a core issue in network research. Assessing the controllability robustness of networks under destructive attacks holds significant practical importance. This paper studies the controllability of networks from the perspective of malicious attacks. A novel attack model is proposed to evaluate and challenge network controllability. This method disrupts network controllability with high precision by identifying and targeting critical candidate nodes. The model is compared with traditional attack methods, including degree-based, betweenness-based, closeness-based, pagerank-based, and hierarchical attacks. Results show that the model outperforms these methods in both disruption effectiveness and computational efficiency. Extensive experiments on both synthetic and real-world networks validate the superior performance of this approach. This study provides valuable insights for identifying key nodes crucial for maintaining network controllability. It also offers a solid framework for enhancing network resilience against malicious attacks.

Analyzing the Robustness of Complex Networks with Attack Success Rate

Analyzing the robustness of networks against random failures or malicious attacks is a critical research issue in network science, as it contributes to enhancing the robustness of beneficial networks and effectively dismantling harmful ones. Most studies commonly neglect the impact of the attack success rate (ASR) and assume that attacks on the network will always be successful. However, in real-world scenarios, attacks may not always succeed. This paper proposes a novel robustness measure called Robustness-ASR (RASR), which utilizes mathematical expectations to assess network robustness when considering the ASR of each node. To efficiently compute the RASR for large-scale networks, a parallel algorithm named PRQMC is presented, which leverages randomized quasi-Monte Carlo integration to approximate the RASR with a faster convergence rate. Additionally, a new attack strategy named HBnnsAGP is introduced to better assess the lower bound of network RASR. Finally, the experimental results on six representative real-world complex networks demonstrate the effectiveness of the proposed methods compared with the state-of-the-art baselines.

Robustness of Network Controllability with Respect to Node Removals Based on In-Degree and Out-Degree

Network controllability and its robustness have been widely studied. However, analytical methods to calculate network controllability with respect to node in- and out-degree targeted removals are currently lacking. This paper develops methods, based on generating functions for the in- and out-degree distributions, to approximate the minimum number of driver nodes needed to control directed networks, during node in- and out-degree targeted removals. By validating the proposed methods on synthetic and real-world networks, we show that our methods work reasonably well. Moreover, when the fraction of the removed nodes is below 10% the analytical results of random removals can also be used to predict the results of targeted node removals.