Following an analytically predicted energy diagram, we numerically investigate the behavior of a soliton molecule in terms of its energy with respect to the breathing factor and average-dispersion of dispersion managed optical fiber lines. We demonstrate the stable families of soliton molecules in anomalous, normal and zero average dispersion regimes. For normal average dispersion, it is showed that each stable family of SM is distributed over a lower and an upper branches. Further, the stability range is limited by a threshold value and a higher value of the breathing factor. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.