The conductivity of an acetic acid solution generally increases as concentration is increased. The more acetic acid is dissolved in water, the higher the chance of there being acetic acid molecules that dissociate into positive and negative hydronium and acetyl groups that conduct electricity.
Acetic acid is a weakly dissociating acid. When it is added to pure water, it participates in a reversible reaction forming hydronium and acetyl groups that are free to move within the solution. These groups are continuously being generated and recombined. As the concentration of the acetic acid increases, there arises a higher likelihood for its dissociation into hydronium and acetyl groups, assuming there are sufficient water molecules to react with the molecular acetic acid. The increase in solution conductivity that accompanies the increase in conducting species with increasing concentration holds true for low to moderate concentrations.
As the concentration of the acetic acid overtakes that of water, the conductivity begins to decrease again. This is because a solution where the acetic acid is the majority component does not have as many water molecules to react with, enabling it to dissociate and form conducting species. Pure acetic acid has zero conductivity, because all molecules exist in un-dissociated form.