Users don't need to worry about routing when they connect to the internet, though in fact the computer is making 10+ hops for any given connection.
Lightning will work the same way. Nobody needs to worry about graph theory, they can just generally assume that the graph is fully connected, and that their software will be able to find a path from A to B.
The internet is not decentralized the way Bitcoin is. Actually I'd argue that the internet is more like the modern banking system: you have big corporations (ISPs, Google, Facebook, Netflix, Amazon...) interconnecting to provide a service to users in exchange for money. They have a vested interest in making sure the network actually works, at least for them. If you want to use the Visa payment system you need a bank account, if you want an internet connection you need an ISP. Bitcoin has nothing like that.
What will be bitcoin's "ISPs"? Who makes sure the graph remains connected and usable? Who invests in the "infrastructure", making sure channels remain well balanced? Some say that Lightning will be self-balancing through a clever set of incentives, but that's again extremely experimental and untested.
Also note the big "net neutrality" thing going on in the US right now. What will prevent big players from teaming up and interconnecting with each other to facilitate transactions while leaving out the rest?
I don't have the answers to any of these questions, maybe it's just FUD. I'm just surprised that bitcoin is a couple of weeks from making such a huge jump into the unknown. It's extremely interesting to be sure, but I feel like some people are going to get severely hurt if this whole thing comes crashing down.
I don't see a reason that exchanges couldn't take on the role of ISP/bank in this situation. Essentially you have an account with 1500 BTC at an exchange, and you say that you want to put 500BTC into a lightning network. Then the bank centralizes itself in the lightning network graph by making connections with other large banks and some major companies.
Of course what we've just done is recreated the modern centralized payment processing scheme on top of the bitcoin network (ie. a mom and pop shop connects to square connects to BoA has my money which doesn't actually exist anywhere, and they make ledger changes and top up later).
You might even be able to make such a system work with no additional transaction fees. But I'm not sure of that.
Lightning will work the same way. Nobody needs to worry about graph theory, they can just generally assume that the graph is fully connected, and that their software will be able to find a path from A to B.