Thresholding normally distributed data creates complex networks

Published in arXiv, 2019

Recommended citation: George Cantwell, Yanchen Liu, Benjamin Maier, Alice Schwarze, Carlos Serv{\'{a}}n, Jordan Snyder, Guillaume St-Onge, "Thresholding normally distributed data creates complex networks." arXiv, 2019.

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 generative model for continuous valued 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, even though the underlying data is not "complex". In particular, we observe heavy-tailed degree distributions, large numbers of triangles, and short path lengths, while we do not observe non-vanishing clustering or community structure.

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