Model-free hidden geometry of complex networks

The fundamental idea of embedding a network in metric space is rooted the principle proximity preservation. Nodes are mapped into points with pairwise distance that reflects their network. Popular methods employed either rely on implicit approximations preservation or implement it by enforcing geometry space, thus hindering geometric properties networks may spontaneously exhibit. Here, we take advantage model-free method explicitly devised for preserving proximity, and characterize emerging from mapping several networks, both real synthetic. We show learned has simple intuitive interpretations: node center representative its closeness centrality, relative positions nodes reflect community structure Proximity can be preserved relatively low-dimensional spaces, hidden displays optimal performance guiding greedy navigation regardless specific topology. finally provides natural description contagion processes complex spatiotemporal patterns represented waves propagating to periphery. findings deepen our understanding networks.