Quantifying efficient information exchange in real network flows

Network science enables the effective analysis of real interconnected systems, characterized by a complex interplay between topology and interconnections strength. It is well-known that network affects its resilience to failures or attacks, as well functions. Exchanging information crucial for many systems: internet, transportation networks brain are key examples. Despite introduction measures efficiency analyze flows, i.e. topologies weighted connectivity, here we show they fail capture combined link existence weight. In this letter propose physically-grounded estimator flow which can be computed every network, regardless from scale nature weights any (missing) metadata. Remarkably, results our captures heterogeneity flows along with topological differences complement obtained percolation several empirical including transportation, trade, migrations, networks. We cutting heaviest connections may increase average communication system hence, counterintuively, sparser not necessarily less efficient. comparison arising different fields, without possible pitfalls deriving flow.