2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171491In this paper we study the uniqueness of expanding self-similar solutions to the network flow in a fixed topological class. We prove the result via the parabolic Allen-Cahn approximation proved in \cite{triodginz}. Moreover, we prove that any regular evolution of connected tree-like network (with an initial condition that might be not regular) is unique in a given a topological class.18 pages, 3 figuresAnalysis of PDEs35K65, 53C44text