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Networks are universally considered as complex structures of interactions oflarge multi-component systems. In order to determine the role that each nodehas inside a complex network, several centrality measures have been developed.Such topological features are also important for their role in the dynamicalprocesses occurring in networked systems. In this paper, we argue that thedynamical activity of the nodes may strongly reshape their relevance inside thenetwork making centrality measures in many cases misleading. We show that whenthe dynamics taking place at the local level of the node is slower than theglobal one between the nodes, then the system may lose track of the structuralfeatures. On the contrary, when that ratio is reversed only global propertiessuch as the shortest distances can be recovered. From the perspective ofnetworks inference, this constitutes an uncertainty principle, in the sensethat it limits the extraction of multi-resolution information about thestructure, particularly in the presence of noise. For illustration purposes, weshow that for networks with different time-scale structures such as strongmodularity, the existence of fast global dynamics can imply that preciseinference of the community structure is impossible.

Indetermination of networks structure from the dynamics perspective