Quantifying randomness in real networks

TL;DR

This paper uses the $dk$-series to analyze the balance of order and randomness in real networks, showing that many properties can be explained by fixed local characteristics and randomness.

Contribution

It introduces the use of the $dk$-series to quantify network randomness and demonstrates its effectiveness across diverse real-world networks.

Findings

Many network properties are reproduced by $dk$-random graphs.

$dk$-series captures key local and global network features.

Software for generating $dk$-random graphs is provided.

Abstract

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the $dk$-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks---the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain---and find that many important local and global structural properties of these networks are closely reproduced by $dk$-random graphs whose degree distributions, degree correlations, and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate $dk$-random graphs.