Node centralities play a pivotal role in network science, social network analysis, and recommender systems. In temporal data, static path-based centralities like closeness or betweenness can give misleading results about the true importance of nodes in a temporal graph. To address this issue, temporal generalizations of betweenness and closeness have been defined that are based on the shortest time-respecting paths between pairs of nodes.

Temporal networks are widely used as abstract graph representations for real-world dynamic systems. Indeed, recognizing the network evolution states is crucial in understanding and analyzing temporal networks. For instance, social networks will generate the clustering and formation of tightly-knit groups or communities over time, relying on the triadic closure theory. However, the existing methods often struggle to account for the time-varying nature of these network structures, hindering their performance when applied to networks with complex evolution states. To mitigate this problem, we propose a novel framework called ESSEN, an Evolution StateS awarE Network, to measure temporal network evolution using von Neumann entropy and thermodynamic temperature. The developed framework utilizes a von Neumann entropy aware attention mechanism and network evolution state contrastive learning in the graph encoding. In addition, it employs a unique decoder the so-called Mixture of Thermodynamic Experts (MoTE) for decoding. ESSEN extracts local and global network evolution information using thermodynamic features and adaptively recognizes the network evolution states. Moreover, the proposed method is evaluated on link prediction tasks under both transductive and inductive settings, with the corresponding results demonstrating its effectiveness compared to various state-of-the-art baselines.

Multi-Agent Reinforcement Learning (MARL) holds significant promise for enabling cooperative driving among Connected and Automated Vehicles (CAVs). However, its practical application is hindered by a critical limitation, i.e., insufficient fault tolerance against observational faults. Such faults, which appear as perturbations in the vehicles' perceived data, can substantially compromise the performance of MARL-based driving systems. Addressing this problem presents two primary challenges. One is to generate adversarial perturbations that effectively stress the policy during training, and the other is to equip vehicles with the capability to mitigate the impact of corrupted observations. To overcome the challenges, we propose a fault-tolerant MARL method for cooperative on-ramp vehicles incorporating two key agents. First, an adversarial fault injection agent is co-trained to generate perturbations that actively challenge and harden the vehicle policies. Second, we design a novel fault-tolerant vehicle agent equipped with a self-diagnosis capability, which leverages the inherent spatio-temporal correlations in vehicle state sequences to detect faults and reconstruct credible observations, thereby shielding the policy from misleading inputs. Experiments in a simulated highway merging scenario demonstrate that our method significantly outperforms baseline MARL approaches, achieving near-fault-free levels of safety and efficiency under various observation fault patterns.

Dynamic facial expression recognition (DFER) aims to identify emotional states by modeling the temporal changes in facial movements across video sequences. A key challenge in DFER is the many-to-one labeling problem, where a video composed of numerous frames is assigned a single emotion label. A common strategy to mitigate this issue is to formulate DFER as a Multiple Instance Learning (MIL) problem. However, MIL-based approaches inherently suffer from the visual diversity of emotional expressions and the complexity of temporal dynamics. To address this challenge, we propose TG-DFER, a text-guided weakly supervised framework that enhances MILbased DFER by incorporating semantic guidance and coherent temporal modeling. We incorporate a vision-language pre-trained (VLP) model is integrated to provide semantic guidance through fine-grained textual descriptions of emotional context. Furthermore, we introduce visual prompts, which align enriched textual emotion labels with visual instance features, enabling fine-grained reasoning and frame-level relevance estimation. In addition, a multi-grained temporal network is designed to jointly capture short-term facial dynamics and long-range emotional flow, ensuring coherent affective understanding across time. Extensive results demonstrate that TG-DFER achieves improved generalization, interpretability, and temporal sensitivity under weak supervision. Introduction Facial expressions serve as direct indicators of human emotions, playing a crucial role in interpreting feelings during human interactions [4, 5]. Recognizing these expressions is essential in various fields, including human-computer interaction (HCI) [1], health assessment [2], and driver assistance systems [3].

Graph models help understand network dynamics and evolution. Creating graphs with controlled topology and embedded partitions is a common strategy for evaluating community detection algorithms. However, existing benchmarks often overlook the need to track the evolution of communities in real-world networks. To address this, a new community-centered model is proposed to generate customizable evolving community structures where communities can grow, shrink, merge, split, appear or disappear. This benchmark also generates the underlying temporal network, where nodes can appear, disappear, or move between communities. The benchmark has been used to test three methods, measuring their performance in tracking nodes' cluster membership and detecting community evolution. Python libraries, drawing utilities, and validation metrics are provided to compare ground truth with algorithm results for detecting dynamic communities.

Indeed, recognizing the network evolution states is crucial in understanding and analyzing temporal networks.

Employee turnover is a critical challenge in financial markets, yet little is known about the role of professional networks in shaping career moves. Using the Hong Kong Securities and Futures Commission (SFC) public register (2007-2024), we construct temporal networks of 121,883 professionals and 4,979 firms to analyze and predict employee departures. We introduce a graph-based feature propagation framework that captures peer influence and organizational stability. Our analysis shows a contagion effect: professionals are 23% more likely to leave when over 30% of their peers depart within six months. Embedding these network signals into machine learning models improves turnover prediction by 30% over baselines. These results highlight the predictive power of temporal network effects in workforce dynamics, and demonstrate how network-based analytics can inform regulatory monitoring, talent management, and systemic risk assessment.

Temporal networks have gained significant prominence in the past decade for modelling dynamic interactions within complex systems. A key challenge in this domain is Temporal Link Prediction (TLP), which aims to forecast future connections by analysing historical network structures across various applications including social network analysis. While existing surveys have addressed specific aspects of TLP, they typically lack a comprehensive framework that distinguishes between representation and inference methods. This survey bridges this gap by introducing a novel taxonomy that explicitly examines representation and inference from existing methods, providing a novel classification of approaches for TLP. We analyse how different representation techniques capture temporal and structural dynamics, examining their compatibility with various inference methods for both transductive and inductive prediction tasks. Our taxonomy not only clarifies the methodological landscape but also reveals promising unexplored combinations of existing techniques. This taxonomy provides a systematic foundation for emerging challenges in TLP, including model explainability and scalable architectures for complex temporal networks.

Temporal networks allow representing connections between objects while incorporating the temporal dimension. While static network models can capture unchanging topological regularities, they often fail to model the effects associated with the causal generative process of the network that occurs in time. Hence, exploiting the temporal aspect of networks has been the focus of many recent studies. In this context, we propose a new framework for generative models of continuous-time temporal networks. We assume that the activation of the edges in a temporal network is driven by a specified temporal point process. This approach allows to directly model the waiting time between events while incorporating time-varying history-based features as covariates in the predictions. Coupled with a thinning algorithm designed for the simulation of point processes, SimHawNet enables simulation of the evolution of temporal networks in continuous time. Finally, we introduce a comprehensive evaluation framework to assess the performance of such an approach, in which we demonstrate that SimHawNet successfully simulates the evolution of networks with very different generative processes and achieves performance comparable to the state of the art, while being significantly faster.