The myopic best-response adjustment is a strategy updating rule frequently employed in evolutionary congestion games. Adopting this rule, however, may need precise strategy information of players. In this paper, a novel strategy updating rule is proposed by combining the classical best-response adjustment and a designed time-varying inertia. In the proposed rule, we first consider a prediction mechanism that utilizes the frequency of selected resources rather than players’ individual strategies, derived from any given limited-length historical information on past stages, to predict the congestion vector for the next stage. Furthermore, we consider an inertia-based best-response dynamics for the players with time-varying inertia based on the predicted congestion vector so that the players can either jump to the corresponding likely best-response strategy or keep the previous strategy in the next stage. The proposed rule guarantees almost sure convergence to the set of Nash equilibria where the convergence can be examined with the value of inertia. A server allocation problem of network functions virtualization (NFV) is used as the numerical example to verify the validity of the results.

3D human pose estimation (HPE) is crucial due to its extensive applications. While current 3D HPE methods focus on human skeleton topology for accuracy, they often overlook joint angle information, which is vital in 2D-to-3D pose lifting. This paper introduces the Joint Angle Network (JANE) model to leverage joint angle features from 2D poses. We propose an angle graph convolution module to extract joint angle features and a multi-stage parallel fusion module to integrate these features with input image data. Experiments on Human3.6M show that our method improves accuracy by 8.7% and 2.6% over non-spatiotemporal baselines using 2D ground truth and 2D pose detectors, respectively.

Based on the semi-tensor product of matrices, this article considers the demand-side management and state-flipped control of smart grids. Firstly, the smart grids with single-layer and multi-layer power companies can be modelled by a potential game under some specific conditions. Secondly, in the evolutionary process with single-layer power companies, a state-flipped control is proposed such that the evolutionary game converges to the optimal Nash equilibrium. An algorithm is constructed to reduce the control cost and the flipped node set will be found. Then, the corresponding flipped node subsets can be obtained to make as few evolution steps as possible. Finally, the correctness of the theoretical results is verified by numerical simulations.Note to Practitioners—This paper has great practical applications in the demand-side management of smart grids. Considering different loads of each player, we use a weighted network congestion game to model the smart grids. The weights in the game are specific to each player and represent their congestion impact, which is more practical in engineering problems. Then we search for the conditions that this kind of game is a potential game and hence has Nash equilibria. This starting point is different from the existing works. Furthermore, we propose a novel state-flipped control to intervene the game process and make it converge to the optimal objective. Compared with the existing theoretical results, the calculation is more convenient and the Nash equilibrium can be easily found. This paper shows an effective method to solve the demand-side management of smart grids in practice and also provides ideas for other engineering problems in such as resource allocation.

Recent years have seen a rapid growth of machine learning in cheminformatics problems. In order to tackle the problem of insufficient training data in reality, more and more researchers pay attention to data augmentation technology. However, few researchers pay attention to the problem of construction rules and domain information of data, which will directly impact the quality of augmented data and the augmentation performance. While in graph-based molecular research, the molecular connectivity index, as a critical topological index, can directly or indirectly reflect the topology-based physicochemical properties and biological activities. In this paper, we propose a novel data augmentation technique that modifies the topology of the molecular graph to generate augmented data with the same molecular connectivity index as the original data. The molecular connectivity index combined with data augmentation technology helps to retain more topology-based molecular properties information and generate more reliable data. Furthermore, we adopt five benchmark datasets to test our proposed models, and the results indicate that the augmented data generated based on important molecular topology features can effectively improve the prediction accuracy of molecular properties, which also provides a new perspective on data augmentation in cheminformatics studies.

Due to the decentralized and public nature of the blockchain ecosystem, malicious activities on the Ethereum platform impose immeasurable losses on users. At the same time, the transparency of cryptocurrency transactions provides a unique opportunity to analyze illegal activities, such as phishing scams, from a network perspective. Most existing phishing scam detection methods focus primarily on analyzing account interaction networks, which limits their ability to uncover transaction behavior patterns embedded within transaction interactions. To address this, we construct theTransactionSubGraphNetwork (TSGN) by using transaction subgraphs as basic elements and further propose a novel framework for Ethereum phishing account detection. Specifically, we rebuild the graph structures via three well-designed mapping mechanisms, yielding TSGN and its two variants, i.e., Directed-TSGN and Temporal-TSGN, to obtain direction-aware and time-aware transfer flow features. By further incorporating the mapping strategy into transaction multidigraphs, we develop the Multiple-TSGN, which could preserve more transaction flow features while concurrently reducing the time consumption of modeling large-scale networks. TSGN models based on transaction subgraph interactions can capture complex higher-order dependencies, which lay beyond the reach of models that exclusively capture pairwise account interactions. As a general framework, our model can incorporate various feature extraction methods to improve the performance of phishing detection. Extensive experimental results on Ethereum datasets show that our method achieves superior performance in phishing detection, yielding 3.27%$\sim$6.71% relative improvement over previous state-of-the-art.

In this article, the convergence of state-based games (SBGs) with recurrent state equilibria is considered by the semi-tensor product of matrices. First, the state-action profile distribution is obtained by the proposed whole evolution equation of the state and the action profile. Second, two necessary and sufficient conditions are given to ensure the convergence of the SBGs, one of which is the matrix iteration condition and the other is a set of linear matrix inequalities. Then, the finite-time stabilization with probability one of the SBGs can be implemented by designing state feedback control. Finally, numerical simulations are given to verify the correctness of the theoretical results.

Molecular property prediction faces the challenge of limited labeled data as it necessitates a series of specialized experiments to annotate target molecules. Data augmentation techniques can effectively address the issue of data scarcity. In recent years, Mixup has achieved significant success in traditional domains such as image processing. However, its application in molecular property prediction is relatively limited due to the irregular, non-Euclidean nature of graphs and the fact that minor variations in molecular structures can lead to alterations in their properties. To address these challenges, we propose a novel data augmentation method called Mix-Key tailored for molecular property prediction. Mix-Key aims to capture crucial features of molecular graphs, focusing separately on the molecular scaffolds and functional groups. By generating isomers that are relatively invariant to the scaffolds or functional groups, we effectively preserve the core information of molecules. Additionally, to capture interactive information between the scaffolds and functional groups while ensuring correlation between the original and augmented graphs, we introduce molecular fingerprint similarity and node similarity. Through these steps, Mix-Key determines the mixup ratio between the original graph and two isomers, thus generating more informative augmented molecular graphs. We extensively validate our approach on molecular datasets of different scales with several Graph Neural Network architectures. The results demonstrate that Mix-Key consistently outperforms other data augmentation methods in enhancing molecular property prediction on several datasets.

Graph neural networks (GNNs) have achieved remarkable success in various real-world applications. However, recent studies highlight the vulnerability of GNNs to malicious perturbations. Previous adversaries primarily focus on graph modifications or node injections to existing graphs, yielding promising results but with notable limitations. Graph modification attack (GMA) requires manipulation of the original graph, which is often impractical, while graph injection attack (GIA) necessitates training a surrogate model in the black-box setting, leading to significant performance degradation due to divergence between the surrogate architecture and the actual victim model. Furthermore, most methods concentrate on a single attack goal and lack a generalizable adversary to develop distinct attack strategies for diverse goals, thus limiting precise control over victim model behavior in real-world scenarios. To address these issues, we present a gradient-free generalizable adversary that injects a single malicious node to manipulate the classification result of a target node in the black-box evasion setting. Specifically, we model the single-node injection label specificity attack as a Markov decision process (MDP) and propose gradient-free generalizable single node injection attack, namely G2-SNIA, a reinforcement learning framework employing proximal policy optimization (PPO). By directly querying the victim model, G2-SNIA learns patterns from exploration to achieve diverse attack goals with extremely limited attack budgets. Through comprehensive experiments over three acknowledged benchmark datasets and four prominent GNNs in the most challenging and realistic scenario, we demonstrate the superior performance of our proposed G2-SNIA over the existing state-of-the-art baselines. Moreover, by comparing G2-SNIA with multiple white-box evasion baselines, we confirm its capacity to generate solutions comparable to those of the best adversaries.

Critical node detection (CND) is commonly used to detect nodes with a high impact on network robustness. It has been widely used in disease propagation, social networks, communications, and other fields. As a nondeterministic polynomial-time (NP)-complete problem, the efficiency of solving CND severely limits the scale of the available network. Fortunately, the evolutionary algorithm (EA) is an effective method to solve this problem. However, although EA improves the global search capability of the algorithm by preserving gene diversity, it also introduces many inferior genes, thus expanding the candidate solution space, reducing the search efficiency, and making it difficult to apply the pruning algorithm directly to its solution space. Hence, indirectly reducing the solution space of EA by deleting inferior genes is a feasible pruning method; however, the interaction of multiple genes affects the quality of CND solutions, making it a challenge to pick out inferior individual genes. Therefore, this work proposes a multipopulation synergistic gene screening algorithm based on the parallelism of EA and combined with Ensemble learning for identifying low-quality genes and removing them as a way of pruning the solution space of the algorithm and improving the search efficiency. The algorithm encodes all nodes in the graph as the gene pool of EA and treats a single population as a weak learner to screen the dominant genes in the gene pool and achieve fast pruning of EA’s solution space by integrating the dominant individuals in multiple populations. In this work, the experiments demonstrate the effectiveness of the proposed method and analyze the effect of different network structures on the algorithm.

Graph neural network (GNN) has achieved remarkable success in various graph learning tasks, such as node classification, link prediction, and graph classification. The key to the success of GNN lies in its effective structure information representation through neighboring aggregation. However, the attacker can easily perturb the aggregation process through injecting fake nodes, which reveals that GNN is vulnerable to the graph injection attack (GIA). Existing GIA methods primarily focus on damaging the classical feature aggregation process while overlooking the neighborhood aggregation process via label propagation. To bridge this gap, we propose the label-propagation-based global injection attack (LPGIA) which conducts the GIA on the node classification task. Specifically, we analyze the aggregation process from the perspective of label propagation and transform the GIA problem into a global injection label specificity attack problem. To solve this problem, LPGIA utilizes a label-propagation-based strategy to optimize the combinations of the nodes connected to the injected node. Then, LPGIA leverages the feature mapping to generate malicious features for injected nodes. In extensive experiments against representative GNNs, LPGIA outperforms the previous best-performing injection attack method in various datasets, demonstrating its superiority and transferability.

With the rapid development of artificial intelligence, a number of machine learning algorithms, such as graph neural networks (GNNs), have been proposed to facilitate network analysis or graph data mining. Although effective, recent studies show that these advanced methods may suffer from adversarial attacks, i.e., they may lose effectiveness when only a small fraction of links are unexpectedly changed. This article investigates three well-known adversarial attack methods, i.e., Nettack, Meta Attack, and GradArgmax. It is found that different attack methods have their specific attack preferences on changing the target network structures. Such attack patterns are further verified by experimental results on some real-world networks, revealing that, generally, the top-4 most important network attributes on detecting adversarial samples suffice to explain the preference of an attack method. Based on these findings, the network attributes are utilized to design machine learning models for adversarial sample detection and attack method recognition with outstanding performance.

This article studies the impact of constrained optimal stealthy attacks on the state estimator, where man-in-the-middle attacks with a linear form can compromise innovations transmitted through a wireless network. First, a novel resource-constrained attack model is proposed, in which there are only a finite number of attack instants within a fixed interval. Second, the evolution of the estimation error covariance under attacks is obtained, and the covariance at the ultimate instant of the attack interval is regarded as the attacker’s cost function. Moreover, a relaxed condition of the strict stealthiness, named Kullback–Leibler divergence, is employed to describe the attacker’s the stealthiness metric. Third, the one-time and holistic optimization problems of stealthy attacks are solved by exploiting the Lagrange multiplier method. Then the constrained optimal attack strategies are obtained to produce the largest ultimate estimation error covariance. Finally, two simulation cases are provided to confirm the correctness of the designed attack strategies.

The concept of$k$-core in complex networks plays a key role in many applications, e.g., understanding the global structure or identifying central/critical nodes, of a network. A malicious attacker with a jamming ability can exploit the vulnerability of the$k$-core structure to attack the network and invalidate the network analysis methods, e.g., reducing the$k$-shell values of nodes can deceive graph algorithms, leading to the wrong decisions. In this article, we investigate the robustness of the$k$-core structure under adversarial attacks by deleting edges, for the first time. First, we give the general definition of the targeted$k$-core attack, map it to the set cover problem, which is NP-hard, and further introduce a series of evaluation metrics to measure the performance of attack methods. Then, we propose the$Q$index theoretically as the probability that the terminal node of an edge does not belong to the innermost core, which is further used to guide the design of our heuristic attack methods, namely, COREATTACK and GreedyCOREATTACK. The experiments on a variety of real-world networks demonstrate that our methods behave much better than a series of baselines, in terms of much smaller edge change rate (ECR) and false attack rate (FAR), achieving state-of-the-art attack performance. More impressively, for certain real-world networks, only deleting one edge from the$k$-core may lead to the collapse of the innermost core, even if this core contains dozens of nodes. Such a phenomenon indicates that the$k$-core structure could be extremely vulnerable under adversarial attacks, and its robustness, thus, should be carefully addressed to ensure the security of many graph algorithms. An open-source implementation is available athttps://github.com/Yocenly/COREATTACCK.

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the underlying network. Although such statistics can be used to describe a network model, or even to design some network algorithms, the role of subgraphs in such applications can be further explored so as to improve the results. In this article, the concept of subgraph network (SGN) is introduced and then applied to network models, with algorithms designed for constructing the 1st-order and 2nd-order SGNs, which can be easily extended to build higher-order ones. Furthermore, these SGNs are used to expand the structural feature space of the underlying network, beneficial for network classification. Numerical experiments demonstrate that the network classification model based on the structural features of the original network together with the 1st-order and 2nd-order SGNs always performs the best as compared to the models based only on one or two of such networks. In other words, the structural features of SGNs can complement that of the original network for better network classification, regardless of the feature extraction method used, such as the handcrafted, network embedding and kernel-based methods.