A Novel Exploration of Diffusion Process based on Multi-types Galton-Watson Forests

TL;DR

This paper introduces a novel interpretation of diffusion processes using degenerated multi-types Galton-Watson forests, linking them explicitly to systems like Google PageRank and enhancing their convergence properties.

Contribution

It establishes an explicit relationship between diffusion processes and MGWF, offering new insights and improving convergence in PageRank computations.

Findings

Explicit interpretation of diffusion via MGWF

Improved convergence in PageRank system

Validated through experimental results

Abstract

Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. And the multi-types 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-types Galton-Watson forest (MGWF) to interpret the diffusion process and establish an equivalent 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 behaviour of the iterative diffusion process and Google PageRank system. We validate the proposal by experiment while providing new research directions.