Robustness of clustering coefficients

• Published in: Communications in statistics. Theory and methods Vol. 53; no. 20; pp. 7144 - 7180
• Main Authors: Zhao, Xiaofeng, Yuan, Mingao
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 17-10-2024; Taylor & Francis Ltd
• Subjects: average clustering coefficient; Clustering; Erdös-Rényi random graph; Error analysis; Global clustering coefficient; Graph theory; measurement error; power-law random graph; Robustness
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2023.2259525

In analyzing collected network data, measurement error is a common concern. One of the current research interests is to study robustness of network properties to measurement error. In this work, we analytically study the impact of measurement error on the global clustering coefficient and the average clustering coefficient of a network. Two types of common measurement errors are considered: (I) each node is randomly removed with probability β and (II) each edge is randomly removed with probability γ. We analytically derive the limits of the clustering coefficients of an inhomogeneous Erdös-Rényi random graph or a power-law random graph with the above two measurement errors. The limits can be used to quantify robustness of the coefficients: if the limits do not depend on β or γ, the coefficients can be considered as robust. Based on our results, the global clustering coefficient and the average clustering coefficient are robust to random removal of nodes but vulnerable to random removal of edges. Extensive experiments validate our theoretical results.