Understanding how information navigates through nodes of a complex network has become an increasingly pressing problem across scientific disciplines. Several approaches have been proposed on the basis of shortest paths or diffusive navigation. However, no existing approaches have tackled the challenges of efficient communication in networks without full knowledge of their global topology under external noise. Here, we develop a first principles approach and mathematical formalism to determine the informational cost of navigating a network under different levels of external noise. Using this approach we discover the existence of a trade-off between the ways in which networks route information through shortest paths, their entropies and stability, which define three classes of real-world networks. This approach reveals that environmental pressure has shaped the ways in which information is transferred in bacterial metabolic networks and allowed us to determine the levels of noise at which a protein–protein interaction network seems to work in normal conditions in a cell.