Add configuration model generation

[qiemem]

The configuration model takes a specified degree distribution and generates a random network with that exact degree distribution. It works as follows: give each node i k_i link stubs, where a k_i is the degree assigned to node i and a link stub is simply a link with only one end connected. Connect the link stubs to each other uniformly at random. This can result in networks with multiple links between nodes and self-loops. If any appear, just reshuffle the connections.

The nice thing about the configuration model is that it's so flexible. Generating a regular network becomes one line:

nw:generate-configuration n-values 100 [ 5 ]

Arbitrary scale-free networks can be generated like so:

nw:generate-configuration n-values 100 [ round (50 * (? + 1) ^ -1) ]

This is partially inspired by this SO question: http://stackoverflow.com/questions/25332514/assigning-neighbors-to-agents-in-symmetric-manner

[qiemem]

A few things to decide on this:

• Should we add a directed version? That is, it would take both an in-degree and out-degree distribution. If the answer is "yes", then should we allow the undirected version to be used on directed breeds? I'm leaning towards "yes" and "no" respectively.
• What do we do about degree distributions that have no realization? The simplest case is when you have too many required links for the number of nodes. This is easy to detect. However, I don't know how to detect (or if there is) more complicated cases.
• Similarly, some degree distributions will take a long time to realize, simply because the number of pseudo-networks that realize it far outweigh the number of real networks. What do you do in this case? Set a maximum number of attempts and then fail? And then deterministically create a network?

[qiemem]

For the second two points, I realized there's a deterministic way to realize these networks:

1. Sort nodes by degree (highest degree first): v_1, v_2, ..., v_n
2. Iterate down the list so that each node connects with as many nodes as it needs to below itself in the list, skipping any that are full.

If there's a network that realizes the degree distribution, this will realize it.

Then, we can attempt to swap links to randomize. So, we grab two random links and attempt to swap the end of one with an end other the other. Make a bunch of such attempts (some number times the number of links).

I believe this will at least approach a uniform pull from the set of networks with that degree distribution as the number of attempted swaps approaches infinity. Unfortunately, since we can't perform an infinite number of attempted swaps, it will be a different distribution. I'm also not sure if you can work yourself into a network where you can't make any swaps but other realizations exist.

I'm leaning towards implementing this, and then including netlogo code to do actual, guaranteed uniform sampling from the set of realizations for people for whom that's an absolute requirement.