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Volume 563 Issue 7733, 29 November 2018

Clear connections

In many physical networks, such as neurons in the brain or 3D integrated circuits, the nodes and links are themselves physical objects and so cannot intersect or overlap with each other. But the mathematical frameworks used to describe such networks pay scant attention to the actual space occupied by these components and usually fail to account for the ‘no-crossing’ criterion. This effect becomes increasingly important as the packing density of the network increases. In this week’s issue, Nima Dehmamy and his colleagues reveal a theoretical framework that accounts for such physical constraints. This allows the researchers to explore how non-crossing conditions affect a network’s geometry and change the 3D architecture as the packing density alters. The cover image shows two networks laid out in 3D based on the team’s mathematical framework and printed with a 3D printer. On the left is a scale-free network generated by the Barabási–Albert model, while on the right a random network generated by the Erdős–Rényi model.

A.-L. Barabási, N. Dehmamy & A. Grishchenko

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