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

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.