Ah, that's the magic of OpenFlights. Instead of attempting to nail jelly to the wall, I can "crowdsource" my data, so if any airline opens any new route, it'll be added to my database as soon as somebody records their flight. Even right now, with a comparatively paltry ~25,000 flights, it's already surprisingly comprehensive: I can find eg. 152 unique routes from FRA and 100 routes from SIN.

Of course, there are no guarantees of accuracy. Routes are added and removed all the time, and a few people get their jollies by entering non-existent routes -- one guy even had a bit of an art project going on by making a pretty star shape radiating from Midway Island. But with judicious filtering by date and flight count it should be possible to minimize both.