A Novel Exploration of Diffusion Process Based on Multi-Type Galton–Watson Forests

Yanjiao Zhu, Qilin Li, Wanquan Liu (), Chuancun Yin and Zhenlong Gao
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Yanjiao Zhu: School of Statistics and Date Science, Qufu Normal University, Qufu 373165, China
Qilin Li: Department of Computing, Curtin University, Perth 6102, Australia
Wanquan Liu: School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China
Chuancun Yin: School of Statistics and Date Science, Qufu Normal University, Qufu 373165, China
Zhenlong Gao: School of Statistics and Date Science, Qufu Normal University, Qufu 373165, China

Mathematics, 2024, vol. 12, issue 22, 1-14

Abstract: Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. The multi-type Galton–Watson forest is a random model of population growth without space or any other resource constraints. In this paper, we use the degenerated multi-type Galton–Watson forest (MGWF) to interpret the diffusion process, corresponding vertices to types and establishing an equivalence relationship between them. With the two-phase setting of the MGWF, one can interpret the diffusion process and the Google PageRank system explicitly. It also improves the convergence behavior of the iterative diffusion process and Google PageRank system. We validate the proposal by experiment while providing new research directions.

Keywords: diffusion process; stochastic; Galton–Watson forest; Google PageRank system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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