Quantifying randomness in real networks

TLDR

Real networks combine order and disorder, and fixing observed structural properties causes many other properties to emerge as statistical consequences plus additional randomness. The study employs the dk‑series to investigate statistical dependencies between different network properties. The dk‑series provides a complete set of basic characteristics of network structure. dk‑random graphs reproduce many local and global properties of six real networks, and the authors discuss implications and release software to generate such graphs.

Abstract

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.