In this example, we will work on the modularity of the Kato et al. (1990) dataset of plant and pollinator interactions, available from IWDB.

We first save the raw text matrix locally:


If this fails, just download the file manually and save it as kato.txt.

This dataset has 91 plants and about 600 pollinators, and is therefore part of the "big" ecological networks. It is additionally sparse, with about 1200 interactions (for a density of 0.019).

We can read it into a binary adjacency matrix with:

A = map((x) -> x>0?1:0, int(readdlm("kato.txt")))

Once this is done, we will apply the partition_lp to this matrix:

kato_lp = partition_lp(A)

We can measure the modularity of this initial partition using Q:


This should give a value close to 0.54 (keep in mind that this is a stochastic process).

The next step is to optimize the modularity further, using Brim:

kato_lp |> recursive_brim! |> Q

This should give a value around 0.57.

Usually, the LP step is repeated several times, to make sure that a suitably (yet arbitrarily...) large part of the parameter space has been explored. We can do so using a simple wrapper function:

lpbrim = (A) -> A |> partition_lp |> recursive_brim!

Note that this function does not measure modularity. We will first apply it 50 times (on my machine, each run takes on average 3 seconds); of course, for real applications, it would be better to repeat this step 1000 times or more (and to do so in a parallel way).

kato_partitions = map(lpbrim, [A for i in 1:50])

We can now get the modularity values:

kato_partitions_Q = map(Q, kato_partitions)

Most of the times, this will give an array of 50 identical (or very close) values. This is because the modular structure of this network is rather easy to optimize.