Eur. Phys. J. Plus (2022) 137: 381
https://doi.org/10.1140/epjp/s13360-022-02602-0

Regular Article

The emergence of triads on signed social network

¹ School of Electronics and Information Engineering, Taizhou University, 318000, Taizhou, Zhejiang, China
² University of Chinese Academy of Sciences, Academy of Mathematics and Systems Science, CAS - Zhongguancun East Road, Haidian District, Beijing, China

^a lizhenpeng@amss.ac.cn

Received: 11 November 2021
Accepted: 14 March 2022
Published online: 22 March 2022

Abstract

Here, based on classic random graph model, i.e., the probability method, we investigate the emergence of triads in signed random social structure. The provided model shows that the emergence of triads is controlled through a critical threshold probability o(1/N). The triads interval estimation, and balanced and unbalanced triads limit distribution are also provided. We observe that signed social networks in real world are indeed extremely balanced and the number of triads is much higher than that of in background random signed graphs. The evidence of over-represented triads well above random expectations is explainable in terms of the degree distribution high skewness and high average clustering coefficient of empirical observed signed networks. Our proposed model can be used as the background distribution to measure balanced/unbalanced triads level in empirical signed networks. We hope that the results of this paper can be applied to information diffusion, trust prediction, evolutionary public goods game on social medias.