# Thresholding normally distributed data creates complex networks

## TL;DR

This paper investigates how thresholding normally distributed, correlated data can produce network properties typical of complex networks, revealing which features are emergent and which are not.

## Contribution

It introduces a simple correlated data model and analyzes the network properties resulting from thresholding, highlighting which complex network features are emergent.

## Key findings

- Heavy-tailed degree distributions observed
- Large numbers of triangles present
- Short path lengths observed

## Abstract

Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average shortest path lengths. These properties are considered typical of complex networks and appear in many contexts, prompting consideration of their universality. Here we introduce a simple model for correlated relational data and study the network ensemble obtained by thresholding it. We find that some, but not all, of the properties associated with complex networks can be seen after thresholding the correlated data, even though the underlying data are not "complex". In particular, we observe heavy-tailed degree distributions, a large numbers of triangles, and short path lengths, while we do not observe non-vanishing clustering or community structure.