Counting motifs

In this use case, we will count the number of motifs in a food web. Specifically, we will count how many times there is a linear food chain (A→B→C) between three species.

~~~@example motif using EcologicalNetwork

Load a network

N = stony();

List of motifs

m = unipartitemotifs();

The `m` object has 13 different motifs, named as in [Stouffer *et al.*
(2007)][sto]. The function [`unipartitemotifs`](@ref) will generate them when
needed. Let's look at the `m[:S1]` motif:

~~~@example motif
plot_network(m[:S1], file="motifs1.png")

The function to count motifs is called motif, and returns a count: how many triplets of species are in a given conformation. For example:

~~~@example motif s1 = motif(N, m[:S1])

We may be interested in knowing whether this motif is over or under-represented
in the empirical network, compared to a random expectation. To determine this,
we will shuffle interactions around in a way that preserves the number of
interactions*and* the degree distribution of all species, using [`swaps`](@ref).
We will create 100 replicated networks to test.

~~~@example motif
permutations = swaps(N, 100, constraint=:degree)

ms1 = map(x -> motif(x, m[:S1]), permutations)