What does "Closed Walk" mean?
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A closed walk is a path in a graph where you start and end at the same point, visiting other points along the way. Think of it as going for a stroll in a neighborhood where you end up at your front door, even if you took a few detours to check out your neighbors' gardens!
How Does It Work?
In a closed walk, you can visit points multiple times, and you can move in any direction. Picture a dog chasing its tail: it keeps going in circles but always returns to its starting spot. The walk can involve any number of steps, whether you take just a few laps or go for an endless jog.
Application in Graphs
When we talk about graphs (which are just a bunch of points connected by lines), a closed walk can help us understand how things are connected. For example, if points represent cities and lines represent roads, a closed walk shows how you can travel from one city and return without focusing on where you are going next.
Self-Avoiding Polygons
Now, if you want to make things a little more interesting, you can think about self-avoiding polygons. These are paths that do not cross themselves. So, if you imagine a kid drawing a shape with a pencil without lifting it off the paper or retracing any lines, you’ve got the idea! In the world of closed walks, self-avoiding polygons are like the fancy, well-behaved cousins who never run into themselves.
Applications in Real Life
Closed walks can be found in many fields, from computer science to economics. They help us model everything from social networks to how money flows in an economy. So, next time you see a graph, just remember that closed walks might be at play, trying to find their way home!