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Dynamics impose limits to detectability of network structure

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posted on 2022-12-08, 14:37 authored by Malbor Asllani, Bruno Requião da Cunha, Ernesto Estrada, James GleesonJames Gleeson
Networks are universally considered as complex structures of interactions of large multi-component systems. To determine the role that each node has inside a complex network, several centrality measures have been developed. Such topological features are also crucial 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. By proposing a generalisation of the communicability function, 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, hidden global properties such as the shortest path distances can be recovered only in the limit where network-level dynamics are negligible compared to node-level dynamics. From the perspective of network inference, this constitutes an uncertainty condition, 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.

Funding

Study on Aerodynamic Characteristics Control of Slender Body Using Active Flow Control Technique

Japan Society for the Promotion of Science

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Dynamics of the metabolic state in the context of a systematic approach to the study of the processes of growth and development of higher plants and fungi

Russian Foundation for Basic Research

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Development of theoretical and experimental criteria for predicting the wear resistance of austenitic steels and nanostructured coatings based on a hard alloy under conditions of erosion-corrosion wear

Russian Foundation for Basic Research

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History

Publication

New Journal of Physics;22, 063037

Publisher

IOP Publishing

Note

peer-reviewed

Other Funding information

SFI, ERC

Language

English

Also affiliated with

  • MACSI - Mathematics Application Consortium for Science & Industry

Department or School

  • Mathematics & Statistics

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