What are Geodesics? | Graph Theory?

A geodesic is like the shortest path between two places on a curvy surface, think of it as the “straight line” on something that isn’t flat.

Imagine you’re playing with a ball. If you draw a straight line from one point to another on the ball, it looks curved when you look at it from above. That’s a geodesic, the shortest path between two points on the surface of the ball.

Now, in graph theory, which is like a map made up of dots (called vertices) and lines connecting them (called edges), a geodesic becomes the shortest route from one dot to another. It’s like finding the quickest way through a maze or city with roads, you pick the path that has the fewest steps or the least distance.

Think of your favorite toy map, maybe it’s a city or a forest. If you want to go from your house to the park, and there are two paths: one is long and winding, the other is short and direct, the geodesic would be that direct path.

So whether it's on a ball, a map, or even in space, geodesics help us find the quickest way from one place to another.