# Critical Nodes Identification in Complex Networks: A Survey

arXiv: https://arxiv.org/abs/2507.06164 · HTML: https://mlsanity.com/paper/2507.06164/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 346 references that are in the map.
- First posted on arXiv 8 Jul 2025.

## Builds on (most cited first, 30 of 44)

- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Estimating Node Importance in Knowledge Graphs Using Graph Neural Networks](https://mlsanity.com/paper/1905.08865/) (2019)
- [Deep Graph Representation Learning and Optimization for Influence Maximization](https://mlsanity.com/paper/2305.02200/) (2023)
- [Link Prediction in Social Networks: the State-of-the-Art](https://mlsanity.com/paper/1411.5118/) (2014)
- [A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization](https://mlsanity.com/paper/2211.03074/) (2022)
- [Three hypergraph eigenvector centralities](https://mlsanity.com/paper/1807.09644/) (2018)
- [DISCO: Influence Maximization Meets Network Embedding and Deep Learning](https://mlsanity.com/paper/1906.07378/) (2019)
- [ToupleGDD: A Fine-Designed Solution of Influence Maximization by Deep Reinforcement Learning](https://mlsanity.com/paper/2210.07500/) (2022)
- [Identifying a set of influential spreaders in complex networks](https://mlsanity.com/paper/1602.00070/) (2016)
- [Scalable Graph Neural Network-based framework for identifying critical nodes and links in Complex Networks](https://mlsanity.com/paper/2012.15725/) (2020)
- [MultiImport: Inferring Node Importance in a Knowledge Graph from Multiple Input Signals](https://mlsanity.com/paper/2006.12001/) (2020)
- [Deep Structural Knowledge Exploitation and Synergy for Estimating Node Importance Value on Heterogeneous Information Networks](https://mlsanity.com/paper/2402.12411/) (2024)
- [Localization and centrality in networks](https://mlsanity.com/paper/1401.5093/) (2014)
- [Discovery of Important Crossroads in Road Network using Massive Taxi Trajectories](https://mlsanity.com/paper/1407.2506/) (2014)
- [The role of centrality for the identification of influential spreaders in complex networks](https://mlsanity.com/paper/1404.4528/) (2014)
- [The Physics of Financial Networks](https://mlsanity.com/paper/2103.05623/) (2021)
- [A centrality measure for quantifying spread on weighted, directed networks](https://mlsanity.com/paper/2303.09684/) (2023)
- [Optimizing Pinning Control of Complex Dynamical Networks Based on Spectral Properties of Grounded Laplacian Matrices](https://mlsanity.com/paper/1804.10818/) (2018)
- [Label Informed Contrastive Pretraining for Node Importance Estimation on Knowledge Graphs](https://mlsanity.com/paper/2402.17791/) (2024)
- [Locating influential nodes via dynamics-sensitive centrality](https://mlsanity.com/paper/1504.06672/) (2015)
- [Identifying influential spreaders in complex networks based on gravity formula](https://mlsanity.com/paper/1505.02476/) (2015)
- [Eigenvector-Based Centrality Measures for Temporal Networks](https://mlsanity.com/paper/1507.01266/) (2015)
- [Top influencers can be identified universally by combining classical centralities](https://mlsanity.com/paper/2006.07657/) (2020)
- [Identifying influential nodes in complex networks: Effective distance gravity model](https://mlsanity.com/paper/2011.06348/) (2020)
- [Identifying Influential Spreaders by Weighted LeaderRank](https://mlsanity.com/paper/1306.5042/) (2013)
- [Leveraging local h-index to identify and rank influential spreaders in networks](https://mlsanity.com/paper/1708.09532/) (2017)
- [Parameterized Complexity of Critical Node Cuts](https://mlsanity.com/paper/1503.06321/) (2015)
- [Three faces of node importance in network epidemiology: Exact results for small graphs](https://mlsanity.com/paper/1708.06456/) (2017)
- [Influencers identification in complex networks through reaction-diffusion dynamics](https://mlsanity.com/paper/1803.01212/) (2018)

## Built on by (most cited first, 2 of 2)

- [Taming Epilepsy: Mean Field Control of Whole-Brain Dynamics](https://mlsanity.com/paper/2603.18035/) (2026)
- [Testing Central Structure for Complex Networks](https://mlsanity.com/paper/2610.15659/) (2026)

## Abstract (arXiv)

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.