Network nestedness as generalized core-periphery structures

TL;DR

This paper demonstrates that nestedness in ecological and economic networks is essentially a form of core-periphery structure, revealing a strong correlation but also underlying restrictions due to degree distributions.

Contribution

It establishes a formal link between nestedness and core-periphery structures and introduces measures for both in weighted and bipartite networks, highlighting fundamental structural constraints.

Findings

Strong correlation between nestedness and core-periphery-ness

Degree distribution restricts nestedness and core-periphery parameter space

Fundamental network properties influence nestedness and core-periphery structures

Abstract

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.