Okay, so I’ve been messing around with this “small world” network thing, and I gotta say, it’s pretty wild. I wanted to see if I could actually build one myself, just to understand it better. So, I started by grabbing a piece of paper and drawing a big circle. Inside that circle, I drew a bunch of dots – these were going to be my “nodes,” like people in a social network, or cities, or whatever.
Then, I connected all these dots to their closest neighbors. I just drew lines between the dots that were physically near each other on the paper. It looked like a neatly organized web at this point, very regular, very predictable.
Making it a “Small World”
But here’s the kicker – that’s not a small world yet. In a real small world, you have those random connections, those “shortcuts” that link people who are otherwise far apart. Think about it – you might know someone in another country, even though most of your friends are local. That’s what I needed to add.
So, I took my pen and started adding some completely random lines. I just picked dots at random and connected them, no matter how far apart they were on the circle. I did this a few times, maybe 5 or 6 random connections for, like, 20 dots. It started to look messy, but that’s the point!
After adding some random connections, I started to check the effect.
- Firstly,I chose two dots randomly.
- Then,I found the shortest way between the two dots by my eyes, and I counted the steps.
- Thirdly, I compared the steps before and after I add the random links. It’s less!
It’s kind of amazing how just a few of these random links can totally change the whole thing. It makes the “distance” between any two dots much smaller, on average. It became a small world, well, on my paper at least!
I didn’t do any fancy math or coding, just a pen and paper experiment. But it really helped me visualize how these networks work. I get it now – it’s all about those unexpected connections that make the world feel so much smaller than it really is. Cool stuff, huh?