# Indetermination of networks structure from the dynamics perspective

## TL;DR

This paper explores how the dynamical activity at local and global levels affects the ability to infer network structure, revealing an uncertainty principle that limits structural reconstruction especially under certain time-scale conditions.

## Contribution

It introduces the concept that local node dynamics can mislead structural importance measures and establishes an uncertainty principle for network inference based on dynamical time scales.

## Key findings

- Local dynamics can distort centrality measures
- Global properties like shortest paths are recoverable under certain conditions
- Fast global dynamics hinder accurate community detection

## Abstract

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