  Understanding the causes and effects of network structural features is a key
task in deciphering complex systems. In this context, the property of network
nestedness has aroused a fair amount of interest as regards ecological
networks. Indeed, Bastolla et al. introduced a simple measure of network
nestedness which opened the door to analytical understanding, allowing them to
conclude that biodiversity is strongly enhanced in highly nested mutualistic
networks. Here, we suggest a slightly refined version of such a measure and go
on to study how it is influenced by the most basic structural properties of
networks, such as degree distribution and degree-degree correlations (i.e.
assortativity). We find that heterogeneity in the degree has a very strong
influence on nestedness. Once such an influence has been discounted, we find
that nestedness is strongly correlated with disassortativity and hence, as
random (neutral) networks have been recently found to be naturally
disassortative, they tend to be naturally nested just as the result of chance.
