  The concept of nestedness, in particular for ecological and economical
networks, has been introduced as a structural characteristic of real
interacting systems. We suggest that the nestedness is in fact another way to
express a mesoscale network property called the core-periphery structure. With
real ecological mutualistic networks and synthetic model networks, we reveal
the strong correlation between the nestedness and core-periphery-ness (likeness
to the core-periphery structure), by defining the network-level measures for
nestedness and core-periphery-ness in the case of weighted and bipartite
networks. However, at the same time, via more sophisticated null-model
analysis, we also discover that the degree (the number of connected neighbors
of a node) distribution poses quite severe restrictions on the possible
nestedness and core-periphery parameter space. Therefore, there must exist
structurally interwoven properties in more fundamental levels of network
formation, behind this seemingly obvious relation between nestedness and
core-periphery structures.
