Complex networks from space-filling bearings

TL;DR

This paper studies the contact networks of space-filling bearings, revealing their bipartite scale-free structure and analyzing key properties like clustering, shortest paths, and percolation.

Contribution

It introduces a hierarchical construction of contact networks for space-filling bearings and provides analytical expressions for their properties.

Findings

Contact networks are bipartite and scale-free.

Clustering coefficient and degree distribution are analytically derived.

Networks exhibit tunable degree exponents and specific percolation behavior.

Abstract

Two dimensional space-filling bearings are dense packings of disks that can rotate without slip. We consider the entire first family of bearings for loops of size four and propose a hierarchical construction of their contact network. We provide analytic expressions for the clustering coefficient and degree distribution, revealing bipartite scale-free behavior with tunable degree exponent depending on the bearing parameters. We also analyze their average shortest path and percolation properties.