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Article

Modeling the Evolution of Dynamic Triadic Closure Under Superlinear Growth and Node Aging in Citation Networks

by
Li Liang
,
Hao Liu
and
Shi-Cai Gong
*
School of Sciences, Zhejiang University of Science and Technology, Hangzhou 310023, China
*
Author to whom correspondence should be addressed.
Entropy 2025, 27(9), 915; https://doi.org/10.3390/e27090915
Submission received: 7 August 2025 / Revised: 25 August 2025 / Accepted: 27 August 2025 / Published: 29 August 2025
(This article belongs to the Topic Computational Complex Networks)

Abstract

Citation networks are fundamental for analyzing the mechanisms and patterns of knowledge creation and dissemination. While most studies focus on pairwise attachment between papers, they often overlook compound relational structures, such as co-citation. Combining two key empirical features, superlinear node inflow and the temporal decay of node influence, we propose the Triangular Evolutionary Model of Superlinear Growth and Aging (TEM-SGA). The fitting results demonstrate that the TEM-SGA reproduces key structural properties of real citation networks, including degree distributions, generalized degree distributions, and average clustering coefficients. Further structural analyses reveal that the impact of aging varies with structural scale and depends on the interplay between aging and growth, one manifestation of which is that, as growth accelerates, it increasingly offsets aging-related disruptions. This motivates a degenerate model, the Triangular Evolutionary Model of Superlinear Growth (TEM-SG), which excludes aging. A theoretical analysis shows that its degree and generalized degree distributions follow a power law. By modeling interactions among triadic closure, dynamic expansion, and aging, this study offers insights into citation network evolution and strengthens its theoretical foundation.
Keywords: citation networks; network evolution; triangular structure; superlinear growth; node aging citation networks; network evolution; triangular structure; superlinear growth; node aging

Share and Cite

MDPI and ACS Style

Liang, L.; Liu, H.; Gong, S.-C. Modeling the Evolution of Dynamic Triadic Closure Under Superlinear Growth and Node Aging in Citation Networks. Entropy 2025, 27, 915. https://doi.org/10.3390/e27090915

AMA Style

Liang L, Liu H, Gong S-C. Modeling the Evolution of Dynamic Triadic Closure Under Superlinear Growth and Node Aging in Citation Networks. Entropy. 2025; 27(9):915. https://doi.org/10.3390/e27090915

Chicago/Turabian Style

Liang, Li, Hao Liu, and Shi-Cai Gong. 2025. "Modeling the Evolution of Dynamic Triadic Closure Under Superlinear Growth and Node Aging in Citation Networks" Entropy 27, no. 9: 915. https://doi.org/10.3390/e27090915

APA Style

Liang, L., Liu, H., & Gong, S.-C. (2025). Modeling the Evolution of Dynamic Triadic Closure Under Superlinear Growth and Node Aging in Citation Networks. Entropy, 27(9), 915. https://doi.org/10.3390/e27090915

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