Link prediction for attributed graphs has garnered significant attention due to its ability to enhance predictive performance by leveraging multi-modal node attributes. However, real-world challenges such as privacy concerns, content restrictions, and attribute constraints often result in nodes facing varying degrees of missing modalities in their attributes, significantly limiting the effectiveness of existing approaches. Building on this fact, we propose a model for linkPRediction in attrIbuted networkSwith uncertainModalities (PRISM), which learns the shared representations across various scenarios of missing modalities through dual-level adversarial training.PRISMcomprises four modules,i.e.,a GCN extractor, an adversarial extractor, an attentive fusion, and an adaptive aggregator. The GCN extractor leverages graph convolutional networks (GCN) to extract fundamental representations from the network topology. The adversarial extractor employs dual-level adversarial training to acquire the shared representations across various multi-modal scenarios at the node-level and link-level, respectively. The attentive fusion applies the multi-head attention mechanism to integrate the shared representations and the fundamental representations. The adaptive aggregator comprehensively considers both node-level and link-level representations to predict the existence of links. Experimental evaluation using real-world datasets demonstrates thatPRISMsignificantly outperforms existing state-of-the-art link prediction methods for multi-modal attributed graphs under missing modalities by improving the Recall@50 metric (R@50) by up to 38.79%.

Understanding structural regularities across layers in multi-layer networks is essential for uncovering their underlying generative mechanisms. While link prediction has been widely explored in multi-layer networks, it is typically treated as an isolated technical problem, often missing its broader implications for network structure and the mechanisms driving edge formation. In this article, we investigate the extent to which network layers exhibit shared generative regularities. By examining the alignment of latent representations across layers, we assess the similarity of their underlying mechanisms and leverage this alignment to improve predictive performance. To facilitate this, we introduce a new metric, C ross- L ayer G enerative C onsistency ( CLGC ), which quantitatively captures the degree of structural and generative alignment between network layers. CLGC is grounded in the shared-latent space framework, positing that layers generated by similar mechanisms will produce compatible latent representations. To realize this approach, we present SupportNet – Support prediction and consistency analysis in multi-layer Net works–a GCN-based model augmented with adversarial training to effectively learn robust shared-latent space representations. These representations support both accurate link prediction and interpretable evaluation of cross-layer generative consistency. Experiments on real-world multi-layer networks demonstrate that SupportNet delivers strong link prediction results improving AUC by 17.47%, AP by 40.41% and AUPR by 39.59% on the Kapferer dataset, while CLGC reveals significant patterns of structural and generative alignment among layers.

Link prediction in multi-layer networks is a longstanding issue that predicts missing links based on the observed structures across all layers. Existing link prediction methods in multi-layer network typically merge the multi-layer network into a single-layer network and/or perform explicit calculations using intra-layer and inter-layer similarity metrics. However, these approaches often overlook the role of coupling in multi-layer networks, specifically the shared information and latent relationships between layers, which in turn limits prediction performance. This calls the need for methods that can extract representations in a shared-latent space to enhance inter-layer information sharing and prediction performance. In this paper, we propose a novel end-to-end framework namely: Link prediction Utilizing Shared-laTent spacE Representation (LUSTER) in multi-layer networks. LUSTER consists of four key modules: the representation extractor, the latent space learner, the complementary enhancer, and the link predictor. The representation extractor focuses on learning the intra-layer representations of each layer, capturing the data characteristics within the layer. The latent space learner extracts representations from the shared-latent space across different network layers through adversarial training. The complementary enhancer combines the intra-layer representations and the shared-latent space representations through orthogonal fusion, providing comprehensive information. Finally, the link predictor uses the enhanced representations to predict missing links. Extensive experimental analyses demonstrate that LUSTER outperforms state-of-the-art methods for link prediction in multi-layer networks, improving the AUC metric by up to 15.87%.

Link prediction in multilayer networks aims to predict missing links at the target layer by incorporating structural information from both auxiliary layers and the target layer. Existing methods tend to learn layer-specific knowledge to maximize the link prediction performance on a specific network layer. However, they have difficulty incorporating multilayer structural information to improve the link prediction performance. Therefore, we propose a Multiple Attention Layer-shareable Method (MALM) for link prediction in multilayer networks, which consists of a feature encoder, a knowledge learner, and a fusion predictor. The feature encoder introduces multiple attention mechanisms to encode the feature representations of links by differentiating the importance of structural information for each link. In cooperation with the feature encoder, the knowledge learner splits the link prediction tasks into different layers and employs meta-learning to learn layer-shareable knowledge from these link prediction tasks. Finally, the fusion predictor combines the learned layer-shareable knowledge with the layer-specific knowledge at the target layer for link prediction. Experiments on real-world datasets demonstrate that the proposed MALM outperforms existing state-of-the-art baselines in link prediction in multilayer networks.

With the rapid expansion of interactions across various domains such as knowledge graphs and social networks, anomaly detection in dynamic graphs has become increasingly critical for mitigating potential risks. However, existing anomaly detection methods often assume noise-free dynamic graphs, overlooking the prevalence of noisy dynamic graphs in real-world applications. Specifically, noisy dynamic graphs affected by structural noises-such as spurious and missing nodes and edges-struggle to consistently provide reliable structural evidence for anomaly detection. To tackle this challenge, we propose an Evolutionary Perception Method (EPM) for identifying anomalous nodes in noisy dynamic graphs by resisting the interference of structural noises. EPM primarily consists of two components: a dynamic fitter and a filtering reviser. The dynamic fitter characterizes the interaction dynamics of nodes that removes and generates links at each period as a multiple superposition state, utilizing various link prediction algorithms to fit evolutionary mechanisms. Additionally, the filtering reviser designs evolutional entropies to quantify the evolutional uncertainty in multiple superposition states, further designing the Kalman filter to optimize these entropies. Extensive experiments show that the proposed EPM method surpasses state-of-the-art approaches in detecting anomalous nodes in noisy dynamic graphs.

Fact-checking fake news detection involves using verified accurate factual information in news reports as "evidence" to validate objective statement "claim". Existing works primarily focus on identifying critical elements within the evidence that support or refute specific claims by assessing the congruence or divergence between the claim and the associated evidence. These methods can broadly be divided into text-based and graph-based-the former centers on understanding the nuances of unstructured text to extract semantic word-level information. At the same time, the latter is proficient at analyzing the node-level structure of graphs it creates from the text to reveal topological insights. Each type provides a distinct view on identifying critical elements for fact-checking. To enhance the complementary nature of the two perspectives, this paper proposes an end-to-end framework for fact-checking fake news detection entitled Multi-view Counterfactual Contrastive Learning (MCCL). The framework incorporates a counterfactual technique to refine the fused features from both the "entity-view" of textual content and the "centrality-view" of the graph structure. Additionally, it employs contrastive learning to sharpen the distinctions among multi-view features, which facilitates the exact identification of critical elements in the evidence related to their respective claims. Experimental results on real datasets demonstrate that the proposed MCCL outperforms state-of-the-art methods.

Link prediction has received increased attention in social network analysis. One of the unique challenges in heterogeneous social networks is link prediction in new link types without verified link information, such as recommending products to new overseas groups. Existing link prediction models tend to learn type-specific knowledge on specific link types and predict missing or future links on the same link types. However, because of the uncertainty of new link types in the evolving process of social networks, it is difficult to collect sufficient verified link information in new link types. Therefore, we propose the Transferable Domain Adversarial Network ( TDAN ) based on transfer learning to handle the challenge. TDAN exploits transferable type-shared knowledge in historical link types to help predict the unobserved links in new link types. TDAN mainly comprises a structural encoder, a domain discriminator, and an optimization decoder. The structural encoder learns the link representations in a heterogeneous social network. Subsequently, to learn transferable type-shared knowledge, the domain discriminator distinguishes link representations into different link types while minimizing the differences between type-specific knowledge in adversarial training. Inspired by the denoising auto-encoder, the optimization decoder reconstructs the learned type-shared knowledge to eliminate the noise generated during the adversarial training. Extensive experiments on Facebook and YouTube show that TDAN can outperform the state-of-the-art models.

The rapid development of heterogeneous networks has proposed new challenges to the long-standing link prediction problem. Existing models trained on the verified edge samples from different types usually learn type-specific knowledge, and their type-specific predictions may be contradictory for unverified edge samples with uncertain types. This challenge is termed edge-type disturbance in link prediction in heterogeneous networks. To address this challenge, we develop a disturbance-resilient prediction method ( DRPM ) comprising a structural characterizer, a type differentiator, and a resilient predictor. The structural characterizer is responsible for learning edge representations for link prediction. Concurrently, the type differentiator distinguishes type-specific edge representations to generate diverse type experts while maximizing their link prediction performances on specific types. Furthermore, the resilient predictor evaluates the reliability weights of different type experts to develop a resilient prediction mechanism to aggregate discriminable predictions. Extensive experiments conducted on various real-world datasets demonstrate the importance of the explainable introduction of the edge-type disturbance and the superiority of DRPM over state-of-the-art methods.

Heterogeneous social networks, which are characterized by diverse interaction types, have resulted in new challenges for missing link prediction. Most deep learning models tend to capture type-specific features to maximize the prediction performances on specific link types. However, the types of missing links are uncertain in heterogeneous social networks; this restricts the prediction performances of existing deep learning models. To address this issue, we propose a multi-type transferable method (MTTM) for missing link prediction in heterogeneous social networks, which exploits adversarial neural networks to remain robust against type differences. It comprises a generative predictor and a discriminative classifier. The generative predictor can extract link representations and predict whether the unobserved link is a missing link. To generalize well for different link types to improve the prediction performance, it attempts to deceive the discriminative classifier by learning transferable feature representations among link types. In order not to be deceived, the discriminative classifier attempts to accurately distinguish link types, which indirectly helps the generative predictor judge whether the learned feature representations are transferable among link types. Finally, the integratedMTTMis constructed on this minimax two-player game between the generative predictor and discriminative classifier to predict missing links based on transferable feature representations among link types. Extensive experiments show that the proposedMTTMcan outperform state-of-the-art baselines for missing link prediction in heterogeneous social networks.

Despite the massive surge of evolving social network analysis in popularity, existing research usually represent the observed social interactions among individuals as completely credible edges. However, due to information inaccuracy, individual non-response and dropout, and sampling biases in observations, the evolving noisy social network that coexists true edges and spurious edges is pervasive in actual applications, where the ignoration of credibility otherness of observed edges could lead to the wrong estimates of social properties and misleading conclusions. To discover credible edge information to shape correct social interactions among individuals, we propose a universal and explainable multiple-neighbor evolutional filtering method (MEFM) to evaluate how credible of observed edges to ‘truly’ exist in the evolving noisy social network.MEFMconsists of an evolutional extractor and a filtering evaluator. To resist the noisy disturbance, the evolutional extractor exploits the evolutional states of edges from the perspective of evolution mechanisms within multiple-neighbor ranges, which applies different link prediction algorithms to fit the evolution mechanism in the formation of each edge. Further, the filtering evaluator reconstructs Kalman filter to predict and refine the evolutional states of edges based on their evolving local structures. As a result,MEFMcombines the evolutional extractor and the filtering evaluator to analyze the evolutional fluctuations of the observed edges to evaluate their credibility. Extensive experiments on real-world datasets demonstrate that our proposedMEFMcan effectively and reasonably evaluate edge credibility in evolving noisy social networks.

Given the distribution difference of the vehicle flow in different urban areas, coordinating the optimization priorities of crossroads in the dynamic control of traffic lights is vital. To reduce traffic congestion at crossroads, in this study, an intelligent diverse optimization priority method (IDOPM) was developed for dynamic traffic light control at crossroads, where diverse optimization priorities can be flexibly and efficiently assigned to different crossroads. The IDOPM mainly consists of a dynamic state constructor and an optimization priority assigner. The dynamic state constructor controls the transformation of the signal combinations of traffic lights. The signal combinations of traffic lights at crossroads are abstracted as cells to be controlled by formulated rules. By designing duration particles and enhancing particles, the optimization priority assigner reconstructs the quantum particle swarm algorithm to assign crossroads with different optimization priorities. The results obtained by comparison with state-of-the-art methods via extensive experiments confirmed the outstanding optimization performance of the proposed IDOPM in dynamic traffic light control.

Recently, dynamic social network research has attracted a great amount of attention, especially in the area of anomaly analysis that analyzes the anomalous change in the evolution of dynamic social networks. However, most of the current research focused on anomaly analysis of the macro representation of dynamic social networks and failed to analyze the nodes that have anomalous structural changes at a micro level. To identify and evaluate anomalous structural change-based nodes in generalized dynamic social networks that only have limited structural information, this research considers undirected and unweighted graphs and develops a multiple-neighbor superposition similarity method ( ), which mainly consists of a multiple-neighbor range algorithm ( ) and a superposition similarity fluctuation algorithm ( ). introduces observation nodes, characterizes the structural similarities of nodes within multiple-neighbor ranges, and proposes a new multiple-neighbor similarity index on the basis of extensional similarity indices. Subsequently, maximally reflects the structural change of each node, using a new superposition similarity fluctuation index from the perspective of diverse multiple-neighbor similarities. As a result, based on and , not only identifies anomalous structural change-based nodes by detecting the anomalous structural changes of nodes but also evaluates their anomalous degrees by quantifying these changes. Results obtained by comparing with state-of-the-art methods via extensive experiments show that can accurately identify anomalous structural change-based nodes and evaluate their anomalous degrees well.

Recently dynamic social networks witnessed a massive surge in popularity, especially in the area of anomaly detection. Although the text-based methods have achieved impressive detection performances, their applications are limited to the social text provided by users. This research focuses on graph-based methods and proposes a universal method for generalized social networks. Different from the existing graph-based methods that summarize a number of structural features, the proposed nodes' evolution diversity inspired method (NEDM) detects anomalies in dynamic social networks from the perspective of diverse evolution mechanisms. More specifically, NEDM applies link prediction algorithms at the micro-level to fit evolution mechanisms followed by the behaviors of nodes, and designs indices to evaluate their fitting degrees in edge removal and generation processes. In addition, the behavior of a node is represented as a quantum superposition state where such behavior follows different evolution mechanisms with uncertain probabilities. We propose a quantum mechanism based particle swarm optimization algorithm (QMPSO) in NEDM. QMPSO determines the optimal observation states of the behaviors of different nodes, and maximally reflects the evolutional fluctuations in the evolution processes of social networks. As a result, NEDM can quantify the evolutional fluctuations in different periods, and detect anomalies in dynamic social networks. Comparing with art-of-the-state methods and real social data in extensive experiments on disparate real-world social networks, we verify the outstanding performance of NEDM in terms of both accuracy and universality.

Based on the performance of entire social networks, anomaly analysis for evolving social networks generally ignores the otherness of the evolutionary behaviors of different nodes, such that it is difficult to precisely identify the anomalous evolutionary behaviors of nodes ( AEBN ). Assuming that a node's evolutionary behavior that generates and removes edges normally follows stable evolutionary mechanisms, this study focuses on detecting and assessing AEBN, whose evolutionary mechanisms deviate from their past mechanisms, and proposes a link prediction detection ( LPD ) method and a matrix perturbation assessment ( MPA ) method. LPD describes a node's evolutionary behavior by fitting its evolutionary mechanism, and designs indexes for edge generation and removal to evaluate the extent to which the evolutionary mechanism of a node's evolutionary behavior can be fitted by a link prediction algorithm. Furthermore, it detects AEBN by quantifying the differences among behavior vectors that characterize the node's evolutionary behaviors in different periods. In addition, MPA considers AEBN as a perturbation of the social network structure, and quantifies the effect of AEBN on the social network structure based on matrix perturbation analysis. Extensive experiments on eight disparate real-world networks demonstrate that analyzing AEBN from the perspective of evolutionary mechanisms is important and beneficial.

Recently, social networks have witnessed a massive surge in popularity. A key issue in social network research is network evolution analysis, which assumes that all the autonomous nodes in a social network follow uniform evolution mechanisms. However, different nodes in a social network should have different evolution mechanisms to generate different edges. This is proposed as the underlying idea to ensure the nodes' evolution diversity in this paper. Our approach involves identifying the micro-level node evolution that generates different edges by introducing the existing link prediction methods from the perspectives of nodes. We also propose the edge generation coefficient to evaluate the extent to which an edge's generation can be explained by a link prediction method. To quantify the nodes' evolution diversity, we define the diverse evolution distance. Furthermore, a diverse node adaption algorithm is proposed to indirectly analyze the evolution of the entire network based on the nodes' evolution diversity. Extensive experiments on disparate real-world networks demonstrate that the introduction of the nodes' evolution diversity is important and beneficial for analyzing the network evolution. The diverse node adaption algorithm outperforms other state-of-the-art link prediction algorithms in terms of both accuracy and universality. The greater the nodes' evolution diversity, the more obvious its advantages.