Introduction to Complex Systems

Prof. Dirk Brockmann, Winter Term 2021

Practical Problem 16: Introduction to Networks

In addition to turtles and patches, netlogo features another type of agent called a link. Links are agents that connect turtles to form turtle networks.

Networks are very important in the study of complex systems, and tomorrow we will cover some basic network science in class. Today, we will start playing with networks in netlogo. Netlogo comes with a number of nice, simple commands connected to networks. Check out the manual for info on the agent type link.

Let's begin

Let us first create a set of $N$ turtles where the number should be between 10 and 300 or so.

crt N [set shape "circle" set color red]

we colored them red, but that's your choice and made the round.

Let's use a new command that is practical here

layout-circle turtles world-width / 4 - 1

This command arranges all the turtles in a circle.

Let's now make a button and call it knut or something like that. Let's write a function that is executed when the button is pressed:

to knut
    ask turtles [
        create-links-with other turtles
    ]   
    ask links [
    if random-float 1 < (1 - p)  [die]
]
end

Please understand what's happening here. The first ask look iterates over all the turtles and creates links with all other turtles.

In the second command we ask all links to die with probability $1-p$.

You should see the links when you press the 'knut' button.

Nice layout

make a new button and call it 'spring'. Make this button into a forever looper. The corresponding function should look like this:

to spring
    repeat 30 [layout-spring turtles links 0.2 5 .01 ]
    tick
end

read the manual on the command layout-spring. This command takes 5 arguments. The first are the nodes of the network (turtles) the second the links. These are usually always those arguments. The next 3 parameters are spring-constant spring-length repulsion-constant

What the spring function does is pretend the links are springs that pull the network together. Each spring has a spring constant. a typical length and the nodes are "electrically charged" so the entire thing doesn't collapse.

Excersise

Extend you program so that the three parameters of the layout-spring function are sliders that you can change.

Dynamic Network

Now let's make this more interesting. Let's make a dynamic network. Write a go function that

picks a random turtle that has at least one link ( ask one-of turtles with [count link-neighbors >0] )

removes one of the links (ask one-of my-links [die])

creates a new link to some other random turtle (create link with one-of other turtles with [link-neighbor? myself = false])

Flockworks

The above dynamic network is mixing. Over time every node connects eventually to all other nodes at some point, and the number of links remains constant, because every time a link is removed another gets added. At any time the network is random, without structure. Let's change that. Modify your network dynamics according to these two rule:

  1. pick a random node A, remove all the links it has
  2. Make a single link to a randomly chosen node B
  3. Also make links to every link-neighbor of B (B's friends) with probability p (slider variable)