Assortative Mixing in Close-Packed Spatial Networks

TL;DR

This paper derives a relation for degree correlations in spatial networks, showing local clustering as the key factor for assortativity, and applies it to various densely-packed atomic and molecular systems.

Contribution

It introduces a general relation linking nearest neighbor degree correlations to local clustering, specifically in close-packed spatial networks, and analyzes their properties.

Findings

Assortative mixing applies to densely-packed atomic/molecular networks.

Derived conditions for linear dependence of degree correlations.

Identified surface effects and classification fingerprints in networks.

Abstract

A general relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks. The characteristics of networks derived from spatial atomic/molecular systems exemplified by self-organized residue networks and block copolymers, atomic clusters and well-compressed polymeric melts are studied. Distributions of statistical properties of the networks are presented. For these densely-packed systems, assortative mixing in the network construction is found to apply, and conditions are derived for a simple linear dependence. Together, these measures (i) reveal patterns that are common to close-packed clusters of atoms/molecules, (ii) identify the type of surface effects prominent in different systems, and (iii) associate fingerprints that may be used to classify networks with varying types of correlations.