#graphtheory We demonstrate that for geometric random graphs the edge-crossing scales with the square of the number of connections (Supplementary Text 4).

#computationalgeometry We establish analytical relations between the number of connections in a spatial network and their total length (Supplementary Text 1).

#neuroscience Reflecting biological resource constraints, we show that progressive-cost models more accurately capture the key properties of brain networks (Fig 5).

#networkscience We introduce a model based on the concept of progressive cost, where adding a new link becomes increasingly expensive as the network becomes denser (Fig 4).

So many broad insights and implications on :

#dataviz We provide an unbiased criterion to filter complex networks that is compliant with common human perception (Fig 1-3)