Do try to speak to them before doing anything, my tree overhung my neighbour's garden, he cut all of the overhanging branches down, then we had high winds and the tree was blown over, this was because all of the weight was on my side of the fence, the result is that the tree will have to be removed now, it's so bent, and is covering a large part of the garden, if they had spoken to me, then we could have pruned both sides at the same time and kept the tree upright!..............