Non-electrolytes

Not all minerals dissolved in the water are electrolytes.
 
Nitrates, which may be in your tapwater, aren't electrolytes. They aren't electrical conductors. E.P.A. regulations stipulate that drinking water may not contain more than 10 ppm nitrate, but sometimes nitrate levels in private well water in agricultural areas can be higher than this public standard.
 
Organic molecules. Some molecules, especially organic ones, retain their molecular structure when they dissolve in water: they don't dissociate into ions. Glucose and other sugars are good examples of non-conductive solutes; so are humic substances like tannins, and other organics like phenols. Organics don't contribute to the general hardness nor to the buffering of the water. These non-electrolytes don't conduct electricity. Dissolved organic substances often called "dissolved organic carbon" or just "DOC" get their own folder in the menu at the left.