If you have two metal electrodes in its own solution - so silver electrodes and silver ions in solution, then the silver anode will oxidize and those ions that go into solution are then reduced at the cathode. No other reaction occurs.
So, at the silver anode:
Ag - e- --> Ag+ (oxidation)
And at the silver cathode, those same ions that were oxidized are reduced:
Ag+ + e- --> Ag