  We study the behaviors of cohomological Hall algebras and relevant subjects
under an edge contraction. Given a quiver with potential and fix an arrow, the
edge contraction is a way to construct a new quiver with potential. We show
that there is an algebra homomorphism between the cohomological Hall algebras
induced by the edge contraction, which preserves the Hopf algebra structure,
Drinfeld double, mutation, and the dimensional reduction, and induces relations
between scattering diagram and Donaldson-Thomas series.
