Table 1.
Summary statistics on the size and fill of collected networks.
Table 2.
Metrics used in a PCA.
Fig 1.
PCA biplots of the two most explanatory principal components.
Each point indicates a single network, and the ellipses are drawn to contain approximately 68% of the points in each network type, i.e., one standard deviation if the points were to follow a bivariate normal distribution. PC1, principal component 1; PC2, principal component 2; PCA, principal component analysis; var., variation.
Fig 2.
Subsetting the points from the top panel of Fig 1 to include only the networks of crime locations, we now color the points according to the city from which each crime network was collected.
Note that, though all crime networks cluster together in Fig 1, those from the same city cluster more tightly, albeit with significant overlap between cities. This indicates that there is additional structure beyond that used to disambiguate crime networks from those of authorship, legislature, etc., and by looking at these finer differences, more subtle distinctions can be made. PC1, principal component 1; PC2, principal component 2; var., variation.
Fig 3.
Left: overlaying more than 500 ecological networks representing either mutualistic or antagonistic interactions, we find that they do not cluster as nicely as the nonecological ones did, suggesting that there is much more variation within ecological network structure than between the classes of nonecological networks examined here. Right: this result holds when the networks are instead labeled according to the specific type of mutualism/antagonism they describe. PC1, principal component 1; PC2, principal component 2; var., variation.
Fig 4.
We compared networks of ecological interactions based on their value of nestedness and modularity.
We randomized each empirical web 1,000 times according to an Erdős–Rényi (top) or configuration model (bottom), each modified slightly to produce only connected graphs (Supporting information). For each of these randomizations, we calculated nestedness [in a variety of ways, including NODF (N.nodf; [20]), overlap (N.olap; [21]), spectral radius (N.rho; [15]), and temperature (N.temp; [5])] and modularity (Q; [4]). We plot here the Z-score of the empirical value for each measure with respect to the 1,000 randomizations. For the Erdős–Rényi randomizations, the only significant (using Welch’s [22] t test; Supporting information) difference is for NODF, showing mutualistic networks to be more nested than antagonistic ones. For the configuration null model, only the Overlap measure of nestedness shows significant differences (Supporting information), but in this case, networks of antagonistic interactions are deemed more nested than those depicting mutualisms. Modularity does not vary significantly between the two types of ecological interaction networks.