Places To Go, and Ways to Get There

Here are two versions of the Königsberg map. On the left is a smaller version of the map you've already seen, and on the right is the version Euler used in his 1735 proof.

Traditional map

Euler's version

Here's what I think is so mind-bendingly cool about this: Euler threw away all the information that didn't matter to the problem.

If all you're concerned with is which bridges you cross, then for all intents and purposes, each land mass can be represented by a point, and each bridge is just a line between two points.

Which is why I say you can think of graph theory as the study of places to go, and ways to get there.