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.

了解信息如何在复杂网络的各个节点之间导航已成为跨科学界日益紧迫的问题。在最短路径或扩散导航的基础上已经提出了几种方法。但是，在没有充分了解外部噪声下其全局拓扑的情况下，没有任何现有方法可以解决网络中有效通信的挑战。在这里，我们开发了第一种原理方法和数学形式主义来确定在不同级别的外部噪声下导航网络的信息成本。使用这种方法，我们发现网络通过最短路径路由信息的方式，其熵和稳定性之间存在权衡关系，这定义了现实世界网络的三类。