Yes. Both of the large positive cables to the starter solenoid should be large. The one from the batt to the solenoid, and the one from the alternator to the solenoid. The reason being is that all running accessories and the battery charging will be handled by that new large wire, and if the alternator is capable of supplying double the current, then you'll need it. It's also safer if you splice a fusible link into the wire between the alternator and the starter solenoid. Anything over 60A would be fine, with a little margin. 100A, or so.
I think I ran 4AWG, which should handle 100A of 12VDC. The "stock" positive battery wire is usually much larger and obviously already sufficient.