Despite various measures across different engineering and social systems, network robustness remains crucial for resisting random faults and malicious attacks. In this study, robustness refers to the ability of a network to maintain its functionality after a part of the network has failed. Existing methods assess network robustness using attack simulations, spectral measures, or deep neural networks (DNNs), which return a single metric as a result. Evaluating network robustness is technically challenging, while evaluating a single metric is practically insufficient. This article proposes a multitask analysis system based on the graph isomorphism network (GIN) model, abbreviated as GIN-MAS. First, a destruction-based robustness metric is formulated using the destruction threshold of the examined network. A multitask learning approach is taken to learn the network robustness metrics, including connectivity robustness, controllability robustness, destruction threshold, and the maximum number of connected components. Then, a five-layer GIN is constructed for evaluating the aforementioned four robustness metrics simultaneously. Finally, extensive experimental studies reveal that 1) GIN-MAS outperforms nine other methods, including three state-of-the-art convolutional neural network (CNN)-based robustness evaluators, with lower prediction errors for both known and unknown datasets from various directed and undirected, synthetic, and real-world networks; 2) the multitask learning scheme is not only capable of handling multiple tasks simultaneously but more importantly it enables the parameter and knowledge sharing across tasks, thus preventing overfitting and enhancing the performances; and 3) GIN-MAS performs multitasks significantly faster than other single-task evaluators. The excellent performance of GIN-MAS suggests that more powerful DNNs have great potentials for analyzing more complicated and comprehensive robustness evaluation tasks.

This paper addresses the robustness of a network to sustain its connectivity and controllability against malicious attacks. This kind of network robustness is typically measured by the time-consuming attack simulation, which returns a sequence of values that record the remaining connectivity and controllability after a sequence of node-or edge-removal attacks. For improvement, this paper develops an efficient framework for network robustness prediction, the spatial pyramid pooling convolutional neural network (SPP-CNN). The new framework installs a spatial pyramid pooling layer between the convolutional and fully-connected layers, overcoming the common mismatch issue in the CNN-based prediction approaches and extending its generalizability. Extensive experiments are carried out by comparing SPP-CNN with three state-of-the-art robustness predictors, namely one CNN-based and two graph neural networks-based frameworks. Synthetic and real-world networks, both directed and undirected, are investigated. Experimental results demonstrate that the proposed SPP-CNN achieves better prediction performances and better generalizability for both cases of known and unknown datasets, with significantly lower time-consumption, than its counterparts.

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.

The connectivity and controllability of complex networks play an important role in ensuring the proper functioning of network systems. Robustness of connectivity and controllability is the ability of a network to maintain its basic functions against various malicious attacks. Convolutional neural network (CNN)-based approaches provide an efficient framework to approximate the network robustness, which significantly reduces computation time compared to attack simulations. In this paper, the performance of CNN-based prediction for connectivity and controllability robustness is investigated, when there are noises in the network input representation. Two CNN-based predictors are compared and investigated, 1) convolutional neural network-based robustness predictor (CNN-RP), and 2) spatial pyramid pooling-based convolutional neural network (CNN-SPP). Two aspects of network information noises are considered and investigated, 1) the random node information noises (RNIN), and 2) the random edge information noises (REIN). The following main conclusions are obtained from extensive experimental studies on synthetic networks: 1) CNN-RP is more tolerant than CNN-SPP to network noises, 2) The characteristics of small-world and scale-free networks make them have a favorable anti-noise ability, and 3) RNIN has less impact on CNN-based prediction performance than REIN, RNIN and REIN show opposite effects on prediction performance when the size of the predicted network is out of the training network size range.

Network robustness is vital in both engineering and social systems to maintain reliability, resilience, and security against various disruptions such as malicious attacks, random failures, and cascading failures. This paper presents a framework called the robustness potential explorer (RPE) to facilitate the study of network robustness. The RPE framework comprises three components: RPE-F, which represents networks using extracted features; RPE-V, which provides visualization; RPE-P, which predicts network robustness enhancement potential. As a case study, the RPE is evaluated by integrating a set of 20 graph features as RPE-F, employing t-distributed stochastic neighbor embedding (t-SNE) as RPE-V, and utilizing three machine learning algorithms as RPE-P. In particular, RPE-V enables meaningful visualization for observing the robustness enhancement process, while RPE-P quantifies the robustness enhancement potential for the given network. Extensive experimental studies demonstrate that the proposed RPE outperforms two state-of-the-art CNN- and GNN-based schemes, with acceptably low prediction errors. These findings highlight the effectiveness of the RPE as a versatile tool for understanding, analyzing, and improving network robustness.

From the perspective of network attackers, finding attack sequences that can cause significant damage to network controllability is an important task, which also helps defenders improve robustness during network constructions. Therefore, developing effective attack strategies is a key aspect of research on network controllability and its robustness. In this paper, we propose a Leaf Node Neighbor-based Attack (LNNA) strategy that can effectively disrupt the controllability of undirected networks. The LNNA strategy targets the neighbors of leaf nodes, and when there are no leaf nodes in the network, the strategy attacks the neighbors of nodes with a higher degree to produce the leaf nodes. Results from simulations on synthetic and real-world networks demonstrate the effectiveness of the proposed method. In particular, our findings suggest that removing neighbors of low-degree nodes (i.e., nodes with degree 1 or 2) can significantly reduce the controllability robustness of networks. Thus, protecting such low-degree nodes and their neighbors during network construction can lead to networks with improved controllability robustness.