# Quantifying randomness in real networks

arXiv: https://arxiv.org/abs/1505.07503 · HTML: https://mlsanity.com/paper/1505.07503/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2015.

## Built on by (most cited first, 3 of 3)

- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [Initialisation and Network Effects in Decentralised Federated Learning](https://mlsanity.com/paper/2403.15855/) (2024)
- [Alice and the Caterpillar: A more descriptive null model for assessing data mining results](https://mlsanity.com/paper/2506.09764/) (2025)

## Abstract (arXiv)

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.