Evolutionary Model of Signed Edges in Online Networks Based on Infinite One-Dimensional Uniform Lattice

Zhenpeng Li (), Zhihua Yan and Xijin Tang
Additional contact information
Zhenpeng Li: School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, Zhejiang, China
Zhihua Yan: School of Management Science and Engineering, Shanxi University of Finance and Economics, Taiyuan 030006, China
Xijin Tang: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100039, China

Mathematics, 2024, vol. 12, issue 7, 1-9

Abstract: The aim of this paper is to study the evolutionary dynamic model for signed edges as observed in online signed social networks. We introduce the incremental mechanism of signed edges behind a simple random walk and explain how this relates to Brownian motion and the diffusive process. We prove how a one-dimensional thermal diffusion equation can be obtained to describe such edge-generating mechanism, and moreover obtain a macroscopic probability distribution of positive and negative edges. The result reveals that the signed edge growth dynamics process can be regarded as a thermodynamic diffusion process. Both empirically and theoretically, we validate that signed network links follow the classic statistic mechanism, i.e., local Brownian motion gives rise to the global emergence pattern of the Gaussian process. The investigation might discover a new and universal characteristic for signed networks, and shed light on some potential applications, such as information spreading, evolutionary games, trust transmission, and dynamic structural balance.

Keywords: random walk; signed network; Brownian motion; diffusive process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/7/1026/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/7/1026/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:7:p:1026-:d:1366756

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().