Critical Nodes Identification in Complex Networks: A Survey

Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research, serving as a vital bridge between theoretical foundations and practical applications. Nevertheless, the intrinsic complexity and structural heterogeneity characterizing real-world networks, with particular emphasis on dynamic and higher-order networks, present substantial obstacles to the development of universal frameworks for critical node identification. This paper provides a comprehensive review of critical node identification techniques, categorizing them into seven main classes: centrality, critical nodes deletion problem, influence maximization, network control, artificial intelligence, higher-order and dynamic methods. Our review bridges the gaps in existing surveys by systematically classifying methods based on their methodological foundations and practical implications, and by highlighting their strengths, limitations, and applicability across different network types. Our work enhances the understanding of critical node research by identifying key challenges, such as algorithmic universality, real-time evaluation in dynamic networks, analysis of higher-order structures, and computational efficiency in large-scale networks. The structured synthesis consolidates current progress and highlights open questions, particularly in modeling temporal dynamics, advancing efficient algorithms, integrating machine learning approaches, and developing scalable and interpretable metrics for complex systems.

Decoupling Spatio-Temporal Prediction: When Lightweight Large Models Meet Adaptive Hypergraphs

Spatio-temporal prediction is a pivotal task with broad applications in traffic management, climate monitoring, energy scheduling, etc. However, existing methodologies often struggle to balance model expressiveness and computational efficiency, especially when scaling to large real-world datasets. To tackle these challenges, we propose STH-SepNet (Spatio-Temporal Hypergraph Separation Networks), a novel framework that decouples temporal and spatial modeling to enhance both efficiency and precision. Therein, the temporal dimension is modeled using lightweight large language models, which effectively capture low-rank temporal dynamics. Concurrently, the spatial dimension is addressed through an adaptive hypergraph neural network, which dynamically constructs hyperedges to model intricate, higher-order interactions. A carefully designed gating mechanism is integrated to seamlessly fuse temporal and spatial representations. By leveraging the fundamental principles of low-rank temporal dynamics and spatial interactions, STH-SepNet offers a pragmatic and scalable solution for spatio-temporal prediction in real-world applications. Extensive experiments on large-scale real-world datasets across multiple benchmarks demonstrate the effectiveness of STH-SepNet in boosting predictive performance while maintaining computational efficiency. This work may provide a promising lightweight framework for spatio-temporal prediction, aiming to reduce computational demands and while enhancing predictive performance. Our code is avaliable at https://github.com/SEU-WENJIA/ST-SepNet-Lightweight-LLMs-Meet-Adaptive-Hypergraphs.

MSCT: Addressing Time-Varying Confounding with Marginal Structural Causal Transformer for Counterfactual Post-Crash Traffic Prediction

Traffic crashes profoundly impede traffic efficiency and pose economic challenges. Accurate prediction of post-crash traffic status provides essential information for evaluating traffic perturbations and developing effective solutions. Previous studies have established a series of deep learning models to predict post-crash traffic conditions, however, these correlation-based methods cannot accommodate the biases caused by time-varying confounders and the heterogeneous effects of crashes. The post-crash traffic prediction model needs to estimate the counterfactual traffic speed response to hypothetical crashes under various conditions, which demonstrates the necessity of understanding the causal relationship between traffic factors. Therefore, this paper presents the Marginal Structural Causal Transformer (MSCT), a novel deep learning model designed for counterfactual post-crash traffic prediction. To address the issue of time-varying confounding bias, MSCT incorporates a structure inspired by Marginal Structural Models and introduces a balanced loss function to facilitate learning of invariant causal features. The proposed model is treatment-aware, with a specific focus on comprehending and predicting traffic speed under hypothetical crash intervention strategies. In the absence of ground-truth data, a synthetic data generation procedure is proposed to emulate the causal mechanism between traffic speed, crashes, and covariates. The model is validated using both synthetic and real-world data, demonstrating that MSCT outperforms state-of-the-art models in multi-step-ahead prediction performance. This study also systematically analyzes the impact of time-varying confounding bias and dataset distribution on model performance, contributing valuable insights into counterfactual prediction for intelligent transportation systems.

Spatio-Temporal Graphical Counterfactuals: An Overview

Counterfactual thinking is a critical yet challenging topic for artificial intelligence to learn knowledge from data and ultimately improve their performances for new scenarios. Many research works, including Potential Outcome Model and Structural Causal Model, have been proposed to realize it. However, their modelings, theoretical foundations and application approaches are usually different. Moreover, there is a lack of graphical approach to infer spatio-temporal counterfactuals, that considers spatial and temporal interactions between multiple units. Thus, in this work, our aim is to investigate a survey to compare and discuss different counterfactual models, theories and approaches, and further build a unified graphical causal frameworks to infer the spatio-temporal counterfactuals.

Interpretable System Identification and Long-term Prediction on Time-Series Data

Time-series prediction has drawn considerable attention during the past decades fueled by the emerging advances of deep learning methods. However, most neural network based methods lack interpretability and fail in extracting the hidden mechanism of the targeted physical system. To overcome these shortcomings, an interpretable sparse system identification method without any prior knowledge is proposed in this study. This method adopts the Fourier transform to reduces the irrelevant items in the dictionary matrix, instead of indiscriminate usage of polynomial functions in most system identification methods. It shows an interpretable system representation and greatly reduces computing cost. With the adoption of $l_1$ norm in regularizing the parameter matrix, a sparse description of the system model can be achieved. Moreover, Three data sets including the water conservancy data, global temperature data and financial data are used to test the performance of the proposed method. Although no prior knowledge was known about the physical background, experimental results show that our method can achieve long-term prediction regardless of the noise and incompleteness in the original data more accurately than the widely-used baseline data-driven methods. This study may provide some insight into time-series prediction investigations, and suggests that an white-box system identification method may extract the easily overlooked yet inherent periodical features and may beat neural-network based black-box methods on long-term prediction tasks.

Identifying Unique Causal Network from Nonstationary Time Series

Identifying causality is a challenging task in many data-intensive scenarios. Many algorithms have been proposed for this critical task. However, most of them consider the learning algorithms for directed acyclic graph (DAG) of Bayesian network (BN). These BN-based models only have limited causal explainability because of the issue of Markov equivalence class. Moreover, they are dependent on the assumption of stationarity, whereas many sampling time series from complex system are nonstationary. The nonstationary time series bring dataset shift problem, which leads to the unsatisfactory performances of these algorithms. To fill these gaps, a novel causation model named Unique Causal Network (UCN) is proposed in this paper. Different from the previous BN-based models, UCN considers the influence of time delay, and proves the uniqueness of obtained network structure, which addresses the issue of Markov equivalence class. Furthermore, based on the decomposability property of UCN, a higher-order causal entropy (HCE) algorithm is designed to identify the structure of UCN in a distributed way. HCE algorithm measures the strength of causality by using nearest-neighbors entropy estimator, which works well on nonstationary time series. Finally, lots of experiments validate that HCE algorithm achieves state-of-the-art accuracy when time series are nonstationary, compared to the other baseline algorithms.