Why Random Links on a Globe Look Directional ✎

Original: "Edge directionality properties in complex spherical networks"
arXiv:1811.05317 · 2018-11-12 · arXiv non-exclusive · independent analysis · 1 min
On a globe, cells near the poles are smaller, which makes random links point the wrong way. A simple weighting fixes that.

A globe is divided into cells: near the equator they are wide, near the poles they are narrow. If you connect random points with lines, the arrows will more often point to where there are more cells, that is, toward the poles. The same happens in networks: nodes near the poles represent smaller areas, so links seem directional when in fact they are random.

Scientists built a network of 18,432 nodes on such a grid and saw that without correction, links in the northern hemisphere point north, and in the southern hemisphere, south. That is an illusion. To remove it, they weighted each link by the area of the neighbor's cell: the larger the area, the greater the weight. After that, the illusion disappeared.

A simple way: multiply the link weight by the cosine of the neighbor's latitude. Then nodes with larger surface areas get more influence, and the picture becomes honest.

Next, they applied the method to real data. In the climate network, atmospheric circulation patterns that transport heat emerged. In the flight network, it became clear where planes actually fly. In the trade network, they saw how countries exchange goods. Now the compass points in the right direction.

In the aviation network, airports on the west coast of the Americas have an average outgoing flight direction to the east, while Asian airports point west, reflecting the asymmetry of trans-Pacific traffic.

Concepts
neural networks in spatial mapping network weight climate network neural networks Graphs navigation edge current topology pattern recognition spatial curvature edge state angle manifold symplectic geometry phylogenetic network spectral pattern boundary geometry edge states