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Article

Critical Node Identification for Cyber–Physical Power Distribution Systems Based on Complex Network Theory: A Real Case Study

by
Mehdi Doostinia
1,
Davide Falabretti
1,*,
Giacomo Verticale
2 and
Sadegh Bolouki
3
1
Electrical Engineering, Department of Energy, Polytechnic University of Milan, 20156 Milan, Italy
2
Department of Electronics, Information, and Bioengineering, Polytechnic University of Milan, 20133 Milan, Italy
3
Department of Computer and Software Engineering, Polytechnique Montréal, Montreal, QC H3T 1J4, Canada
*
Author to whom correspondence should be addressed.
Energies 2025, 18(11), 2937; https://doi.org/10.3390/en18112937
Submission received: 7 April 2025 / Revised: 13 May 2025 / Accepted: 27 May 2025 / Published: 3 June 2025

Abstract

In today’s world, power distribution systems and information and communication technology (ICT) systems are increasingly interconnected, forming cyber–physical power systems (CPPSs) at the core of smart grids. Ensuring the resilience of these systems is essential for maintaining reliable performance under disasters, failures, or cyber-attacks. Identifying critical nodes within these interdependent networks is key to preserving system robustness. This paper applies complex network (CN) theory—specifically degree centrality (DC), closeness centrality (CC), and betweenness centrality (BC)—to a real-world distribution grid integrated with an ICT layer in northeastern Italy. Simulations are conducted across three scenarios: a directed power network, an undirected power network, and an undirected ICT network. Each centrality metric generates a ranking of nodes which is validated using node removal performance (NRP) analysis. In the directed power network, in-closeness centrality and out-degree centrality are the most effective in identifying critical nodes, with correlations of 84% and 74% with NRP, respectively. DC and BC perform best in the undirected power network, with correlation values of 67% and 53%, respectively. In the ICT network, BC achieves the highest correlation (64%), followed by CC at 55%. These findings demonstrate the potential of centrality-based methods for identifying critical nodes and support strategies for enhancing CPPS resilience and fault recovery by distribution system operators.
Keywords: power distribution grids; ICT systems; resilience; cyber–physical power systems; centrality; complex networks power distribution grids; ICT systems; resilience; cyber–physical power systems; centrality; complex networks

Share and Cite

MDPI and ACS Style

Doostinia, M.; Falabretti, D.; Verticale, G.; Bolouki, S. Critical Node Identification for Cyber–Physical Power Distribution Systems Based on Complex Network Theory: A Real Case Study. Energies 2025, 18, 2937. https://doi.org/10.3390/en18112937

AMA Style

Doostinia M, Falabretti D, Verticale G, Bolouki S. Critical Node Identification for Cyber–Physical Power Distribution Systems Based on Complex Network Theory: A Real Case Study. Energies. 2025; 18(11):2937. https://doi.org/10.3390/en18112937

Chicago/Turabian Style

Doostinia, Mehdi, Davide Falabretti, Giacomo Verticale, and Sadegh Bolouki. 2025. "Critical Node Identification for Cyber–Physical Power Distribution Systems Based on Complex Network Theory: A Real Case Study" Energies 18, no. 11: 2937. https://doi.org/10.3390/en18112937

APA Style

Doostinia, M., Falabretti, D., Verticale, G., & Bolouki, S. (2025). Critical Node Identification for Cyber–Physical Power Distribution Systems Based on Complex Network Theory: A Real Case Study. Energies, 18(11), 2937. https://doi.org/10.3390/en18112937

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