Measuring the nestedness of a network
The goal of this use case is to (i) measure the nestedness of a bipartite network and (ii) evaluate whether it differs from the random expectation. We will use the
ollerton data, which are reasonably small, and the
η measure of nestedness (note that
nodf is also available).
using EcologicalNetwork # Get the data in an object N = ollerton(); # We will create a function to return the nestedness of the entire # network instead of an array of nestedness values nest = (x) -> η(x) # We will now generate a series of random networks preserving the degree # distribution S = nullmodel(null2(N)); # There is a function to apply a test rapidly to randomized networks. In this # situation we are interested in testing the fact that the network is more # nested than expected by chance. results = test_network_property(N, nest, S, test=:greater); # We can print the results println( "The original network has a nestedness of ", round(nest(N), 3), ",\n", "which is greater than expected by chance (p ~ ", round(results.pval, 4), ") -- ", results.n, " random networks." )
The original network has a nestedness of 0.641, which is greater than expected by chance (p ~ 0.0) -- 288 random networks.
In this simple example, we used
nullmodel to generate random realizations of a network, and
test_network_property to evaluate whether the observed nestedness was observed by chance. As it stands, all randomized networks had lower values, and so the p-value is (essentially) null. In short, this network is significantly more nested than expected by chance knowing its degree distribution.