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.

EpiLLM: Unlocking the Potential of Large Language Models in Epidemic Forecasting

Advanced epidemic forecasting is critical for enabling precision containment strategies, highlighting its strategic importance for public health security. While recent advances in Large Language Models (LLMs) have demonstrated effectiveness as foundation models for domain-specific tasks, their potential for epidemic forecasting remains largely unexplored. In this paper, we introduce EpiLLM, a novel LLM-based framework tailored for spatio-temporal epidemic forecasting. Considering the key factors in real-world epidemic transmission: infection cases and human mobility, we introduce a dual-branch architecture to achieve fine-grained token-level alignment between such complex epidemic patterns and language tokens for LLM adaptation. To unleash the multi-step forecasting and generalization potential of LLM architectures, we propose an autoregressive modeling paradigm that reformulates the epidemic forecasting task into next-token prediction. To further enhance LLM perception of epidemics, we introduce spatio-temporal prompt learning techniques, which strengthen forecasting capabilities from a data-driven perspective. Extensive experiments show that EpiLLM significantly outperforms existing baselines on real-world COVID-19 datasets and exhibits scaling behavior characteristic of LLMs.

AutoCas: Autoregressive Cascade Predictor in Social Networks via Large Language Models

Popularity prediction in information cascades plays a crucial role in social computing, with broad applications in viral marketing, misinformation control, and content recommendation. However, information propagation mechanisms, user behavior, and temporal activity patterns exhibit significant diversity, necessitating a foundational model capable of adapting to such variations. At the same time, the amount of available cascade data remains relatively limited compared to the vast datasets used for training large language models (LLMs). Recent studies have demonstrated the feasibility of leveraging LLMs for time-series prediction by exploiting commonalities across different time-series domains. Building on this insight, we introduce the Autoregressive Information Cascade Predictor (AutoCas), an LLM-enhanced model designed specifically for cascade popularity prediction. Unlike natural language sequences, cascade data is characterized by complex local topologies, diffusion contexts, and evolving dynamics, requiring specialized adaptations for effective LLM integration. To address these challenges, we first tokenize cascade data to align it with sequence modeling principles. Next, we reformulate cascade diffusion as an autoregressive modeling task to fully harness the architectural strengths of LLMs. Beyond conventional approaches, we further introduce prompt learning to enhance the synergy between LLMs and cascade prediction. Extensive experiments demonstrate that AutoCas significantly outperforms baseline models in cascade popularity prediction while exhibiting scaling behavior inherited from LLMs. Code is available at this repository: https://anonymous.4open.science/r/AutoCas-85C6