
TL;DR
This paper introduces a new, analytically valid normalisation for degree variance in networks, making it unbiased to size and density, and applicable across various network types and real-world data.
Contribution
The authors propose a novel normalisation method for degree variance that is valid for all networks, computationally efficient, and robust to size and density variations.
Findings
Normalised degree variance is unbiased to network size and density.
The new normalisation is consistent across different network models and real-world networks.
It reveals greater degree heterogeneity in biological networks like brain connectomes and food webs.
Abstract
Finding graph indices which are unbiased to network size and density is of high importance both within a given field and across fields for enhancing comparability of modern network science studies. The degree variance is an important metric for characterising network degree heterogeneity. Here, we provide an analytically valid normalisation of degree variance to replace previous normalisations which are either invalid or not applicable to all networks. It is shown that this normalisation provides equal values for graphs and their complements; it is maximal in the star graph (and its complement); and its expected value is constant with respect to density for Erd\"os-R\'enyi (ER) random graphs of the same size. We strengthen these results with model observations in ER random graphs, random geometric graphs, scale-free networks, random hierarchy networks and resting-state brain networks,…
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