Critical Nodes Identification in Complex Networks: A Survey

2025-07-08

AI Summary

Existing approaches for critical node identification in dynamic and higher-order networks lack a unified methodological framework. Method: We systematically survey techniques across social, transportation, biological, and financial domains, and—based on methodological foundations and application contexts—categorize seven mainstream paradigms for the first time. We propose a unified analytical framework explicitly designed for dynamicity and higher-order structural dependencies. Contribution/Results: Our analysis identifies four core challenges: algorithmic generality, real-time evaluability, higher-order dependency modeling, and scalability to large-scale networks. Integrating centrality measures, influence maximization, network control theory, dynamic modeling, and AI-driven methods, we synthesize state-of-the-art advances and delineate three key future directions: time-aware modeling, lightweight and efficient algorithms, and interpretable machine learning integration.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Causality

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Identifying critical nodes in complex networks with diverse applications
• Overcoming complexity and heterogeneity in dynamic and higher-order networks
• Reviewing and classifying methods for critical node identification challenges

Innovation

• Classifies methods into seven main categories
• Highlights algorithmic universality challenges
• Integrates machine learning for complex systems