Watts-Strogatz model
Imagine you have a bunch of friends in a circle and you want to connect them. If you just drew lines directly between them, it would be pretty boring, so instead you decide to use a game of telephone. You tell one friend a message, they tell the next friend, and so on, until eventually the message gets back to you.
Now let's say you want to make this game of telephone more interesting. Instead of connecting your friends in a perfect circle, you randomly choose some friends to disconnect and reconnect with different friends. This means that sometimes the message will travel longer distances and take longer to get back to you, but it also means there are more opportunities for the message to get mixed up or changed along the way.
This is sort of like what the Watts-Strogatz model does. It's a way of creating random networks where some connections are changed and shuffled around. This can lead to some interesting patterns in how information or signals travel through the network. For example, sometimes it will be really easy for information to travel from one part of the network to another, but other times it may get "stuck" in one part and not be able to move much at all.
Overall, the Watts-Strogatz model is a way to explore how randomness and small changes can affect the structure and function of networks. It's a concept that can be used to understand everything from social networks to electrical grids to the internet.
Now let's say you want to make this game of telephone more interesting. Instead of connecting your friends in a perfect circle, you randomly choose some friends to disconnect and reconnect with different friends. This means that sometimes the message will travel longer distances and take longer to get back to you, but it also means there are more opportunities for the message to get mixed up or changed along the way.
This is sort of like what the Watts-Strogatz model does. It's a way of creating random networks where some connections are changed and shuffled around. This can lead to some interesting patterns in how information or signals travel through the network. For example, sometimes it will be really easy for information to travel from one part of the network to another, but other times it may get "stuck" in one part and not be able to move much at all.
Overall, the Watts-Strogatz model is a way to explore how randomness and small changes can affect the structure and function of networks. It's a concept that can be used to understand everything from social networks to electrical grids to the internet.