Loop v.s. nodal analysis of periodic circuit network
I have no idea of how your analysis proceeds from here, however the number of variables is the same. 

Keep in mind that voltage is a relative variable while current is an absolute one. 

When you say the “voltage of the node” you have implicitly added a variable to your system. Your reference “ground” potential, which is not defined for your problem setup and would only show up in the infinite set of initial conditions for the system. 

Instead if you say “the voltage between two nodes” you have removed the need for that arbitrary reference (and it directly relates to the associated current).