Abstract
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.
Highlights
General real-networks analysis In Fig. 2(a) we represent the results for the networks analyzed here in the unit informational square formed by the normalized △S and the ratio of shortest informational paths (SIP) routed through shortest (topological) paths (SP)
In this work we propose a formalism for information transfer” (IT) on networks under external noise
We discover the existence of three main classes of networks: (i) networks operating in mixed states were the diffusing information is naturally routed through shortest paths; (ii) networks operating in pure quantum state were most of information navigates in a purely diffusive way; (iii) networks operating in pure states but were information is routed through SP
Summary
Let us consider the navigation of information on the network illustrated in Fig. 1(a) between the nodes labeled v and w. On “normal” operational conditions there are networks behaving like pure quantum states, for which a complete knowledge of their topology brings no information about the routes of navigation.
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