Figure 1.
Measures of nestedness in networks.
The figure shows three different connectivity matrices with different levels of nestedness as measured by (i) our new nestedness index [Eq. (6)] and (ii) the standard nestedness “temperature’ calculator”. As can be readily seen, the most packed matrix corresponds to a very low temperature and to a high nestedness index () and, reciprocally, the least packed one exhibits a high temperature and an index close to its expected value for a random network (
).
Figure 2.
Correlation coefficient and nestedness in random networks.
(Panel A): Correlation coefficient, , and nestedness
for
networks generated independently using the configuration model with
nodes and
and (from left to right) scale-free (with exponent
), Poissonian, and Gaussian (
) degree distributions. (Panel B): Pearson’s correlation coefficient as a function of network size for scale free networks with
. (Panel C): Averaged nestedness (with error bars corresponding to one standard deviation) as a function of Pearson’s correlation index
in random (scale-free, Poissonian, and Gaussian) networks (as in the left panel). These curves are obtained employing the Wang-Landau algorithm as described in Appendix S3. All three curves show a positive (almost linear) correlation between disassortativity and nestedness: more disassortative networks are more nested. By restricting the corresponding configuration ensembles to their corresponding subsets in which
is kept fixed it is possible to define a more constraint null model as discussed in the main text.
Figure 3.
Correlation coefficient and nestedness in degree-preserving randomiaztions.
Probability distribution of Pearson’s coefficient and of the nestedness coefficient,
, as measured in degree-preserving randomizations of a subset of
(out of a total of
) real empirical networks (as described and referenced in Appendix S5). The actual empirical values in the real network are marked with a black box and compared (also in black) with a segment centered at the mean value of the random ensemble (configuration model) with width equal to one standard deviation. In most cases but not all, the empirical values lie in or near the corresponding interval, suggesting that typically empirical networks are not significantly more assortative/nested than randomly expected.
Figure 4.
Nestedness against assortativity (as measured by Pearson’s correlation coefficient) for data on a variety of networks.
Warm-coloured items correspond to unimodal networks and green ones to bipartite networks of different kinds (see Appendix S5).