Degree Correlations in Random Geometric Graphs

TL;DR

This paper investigates degree correlations in random geometric graphs, revealing how the two-point degree correlation function relates to clustering coefficients in 2D and higher dimensions, advancing understanding of spatial network properties.

Contribution

It introduces new analytical results linking degree correlations to clustering coefficients in random geometric graphs across multiple dimensions.

Findings

Degree correlation functions are expressed in terms of clustering coefficients.

Results extend to arbitrary finite dimensions.

Provides analytical insights into spatial network structure.

Abstract

Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree correlation function in terms of the clustering coefficient of the graphs for two-dimensional space in particular, with extensions to arbitrary finite dimension.