Decanol droplets in a thin layer of sodium decanoate with sodium chloride exhibit bifurcation branching growth due to interplay between osmotic pressure, diffusion and surface tension. We aimed to evaluate if morphology of the branching droplets changes when the droplets are subject to electrical potential difference. We analysed graph-theoretic structure of the droplets and applied several complexity measures. We found that, in overall, the current increases complexity of the branching droplets in terms of number of connected components and nodes in their graph presentations, morphological complexity and compressibility.