  Networks of disparate phenomena-- be it the global ecology, human social
institutions, within the human brain, or in micro-scale protein interactions--
exhibit broadly consistent architectural features. To explain this, we propose
a new theory where link probability is modelled by a log-normal node fitness
(surface) factor and a latent Euclidean space-embedded node similarity (depth)
factor. Modelling based on this theory considerably outperforms popular
power-law fitness and hyperbolic geometry explanations across 110 networks.
Importantly, the degree distributions of the model resemble power-laws at small
densities and log-normal distributions at larger densities, posing a
reconciliatory solution to the long-standing debate on the nature and existence
of scale-free networks. Validating this theory, a surface factor inversion
approach on an economic world city network and an fMRI connectome results in
considerably more geometrically aligned nearest neighbour networks. This
establishes new foundations from which to understand, analyse, deconstruct and
interpret network phenomena.
