The nearest expansion flow of galaxies observed around the Local group is studied as an archetypical example of the newly discovered local expansion flows around groups and clusters of galaxies in the nearby Universe. The flow is accelerating due to the antigravity produced by the universal dark energy background. We introduce a new acceleration measure of the flow which is the dimensionless ``acceleration parameter" Q (x) = x - x^-2 depending on the normalized distance x only. The parameter is zero at the zero-gravity distance x = 1, and Q(x) ∝ x, when x ≫ 1. At the distance x = 3, the parameter Q = 2.9. Since the expansion flows have a self-similar structure in normalized variables, we expect that the result is valid as well for all the other expansion flows around groups and clusters of galaxies on the spatial scales from ˜ 1 to ˜ 10 Mpc everywhere in the Universe.