Complexity and Robustness of Public–Private Partnership Networks

Public-private partnership (PPP) has been increasingly imported to deliver infrastructure and public services around the world. As an emerging public procurement mode, PPP has drawn considerable attention both from academy and industry. We construct a PPP shareholder network of China and analyze its topological complexity, robustness, and geographic structure. We find that the PPP shareholder network exhibits small-world behavior and a heavy-tailed degree distribution. Using multiple centrality measures, we investigate the network robustness under various attack strategies. The results show that the targeted attack destroys the network more efficiently than the random attack, especially the degree-based and betweenness-based attacks. For geographic topology, it exhibits a hierarchical spatial structure in which Beijing is the central hub and provincial capitals are regional centers. Our research has significant implications for policy-making to improve supervision for enterprises involved in PPP projects.

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Publication Details

Journal
Entropy
Published
2026-01-20
DOI
https://doi.org/10.3390/e28010122
Primary Topic
Public-Private Partnership Projects
Type
article
Field-Weighted Citation Impact
0.00

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article

Complexity and Robustness of Public–Private Partnership Networks

Na Zhao, Ling Bai, Xiongfei Jiang
Entropy
Public-Private Partnership Projects
article

Complexity and Robustness of Public–Private Partnership Networks

Na Zhao, Ling Bai, Xiongfei Jiang
article en

Abstract

Public-private partnership (PPP) has been increasingly imported to deliver infrastructure and public services around the world. As an emerging public procurement mode, PPP has drawn considerable attention both from academy and industry. We construct a PPP shareholder network of China and analyze its topological complexity, robustness, and geographic structure. We find that the PPP shareholder network exhibits small-world behavior and a heavy-tailed degree distribution. Using multiple centrality measures, we investigate the network robustness under various attack strategies. The results show that the targeted attack destroys the network more efficiently than the random attack, especially the degree-based and betweenness-based attacks. For geographic topology, it exhibits a hierarchical spatial structure in which Beijing is the central hub and provincial capitals are regional centers. Our research has significant implications for policy-making to improve supervision for enterprises involved in PPP projects.

EntropyVol. 28(1)
Ningbo University (CN)
National Natural Science Foundation of China, Ministry of Education of the People's Republic of China, Ningbo University, Ministry of Education, India, Natural Science Foundation of Zhejiang Province
Partnerships for the goals
Openalex Percentile: Top 85%
Public-Private Partnership Projects
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Complexity and Robustness of Public–Private Partnership Networks — Na Zhao, Ling Bai, et al. · Entropy (2026) | TGRS Research Map | TGRS