What is causing the loud, electrical humming noise in my walls?
Your neighbour must be hearing it as well then, correct? Can you hear it from outside?

First culprits I would look at:


furnace fan or forced exhaust fan
forced exhaust fan of a high-efficiency gas water heater
HRV unit
attic fan
bathroom fan


Ideally you or your neighbour could stand in his/her utility room while the sound is happening, and hopefully narrow it down. Turning off one of those at a time may also help narrow it down. Either way, you're going to have to work with your neighbour to solve it, if you are positive it isn't coming from in your house.