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Pierre
Pierre

Reputation: 387

Node degree in a network

I have a landscape that includes a road network as in the below figure.

enter image description here

I would like to calculate an average number of roads (or white line in the figure) that link each color polygon (for example a black polygon) between them. In a network, a link corresponds to a road, a node corresponds to a color polygon and I think that to calculate an average number of roads between color polygons means to calculate the average node degree of the network. For example, in the figure, the two black polygons are linked by two roads. So, the degree of a black polygon is 2. Is it possible to calculate a node degree with the extension Network of Netlogo ?

Thanks in advance for your help.

Upvotes: 2

Views: 718

Answers (1)

Bryan Head
Bryan Head

Reputation: 12580

Normal NetLogo contains link agents that link turtles even without an extension. Calculating degree is usually just a matter of doing [ count my-links ] of node where node is the turtle you want to know the degree of. However, in NetLogo, turtles can't be connected by more than one link. The typical workaround for this is create a links-own variable (just like turtles-own or patches-own variable) . This variable is often called weight, but you can call it whatever you want. In that case, you would do [ sum [ weight ] of my-links ] of node to calculate the degree.

This is all assuming you have a network representation of your roadways, which it doesn't sound like you do. Furthermore, I'm not sure what you're trying to represent is a network, since (as shown in your picture) roads branch at intersections. Thus more than two polygons could be connected by a single (for some definition of "single") road. This is often called a hypernetwork or hypergraph. However, this is probably a heavier weight concept than what you want.

Now, I'm not entirely sure what you're really trying to calculate. Is it:

  • ...the number of roads connected to a polygon? The lower polygon has 4 roads connected to it, the upper has 3 (visible).
  • ...the number of polygons directly connected to the polygon? Both polygons are connected to 1 other (visible) polygon, though I assume in the larger picture there are more.

The number of roads connected to a polygon would be pretty easy to calculate, assuming each road is 1 pixel wide. You could just do:

count (patch-set [ neighbors4 with [ is-road? ] ] of polygon)

where polygon is a patch set containing the patches of the polygon and is-road? is a reporter that returns true for road patches and false for non-road patches (this could be something pcolor = white). Note that this will break if roads are wider than 1 patch or if the same road can touch a polygon in other places. Let me know if that's the case and I'll expand this into something that can that into account.

The number of polygons directly connected to the polygon is more difficult. The basic idea would be to follow the roads out until you hit other polygons and count the number that you hit. Code for this is somewhat tricky. I think the best way to go about it would be to have two patch-sets, frontier and explored and list of found polygons. frontier should initialize to every road patch touch the polygon. Each iteration, get the polygons touching the frontier and add them to the list of found polygons if they're not already in there. Add the frontier to explored. Get all the road patches touching the frontier that are not in explored. Set the frontier to this new set of patches. Keep going until frontier is empty. This is a version of breadth-first search. There could be a better way to do this.

Upvotes: 1

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