mercury is a liquid and conducts electricity. Do you think it is an electrolyte?
No , mercury is not an electrolyte.
Electrolyte are solutions of ionic compounds for example NaCl or sodium chloride solution is an electrolyte. Here the positive Na ions of sodium metal and negative Chlorine ions are responsible for the conduction of electricity.
However, the case of mercury, Hg ,is different. Though it is liquid, it is a metal. Metals conduct electricity because of the presence of free electrons in their atomic structure. Mercury is not a compound. In general , electrolytes are solutions of ionic compounds