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Network structure from a characterization of interactions in complex systems.

Thorsten Rings^1,2, Timo Bröhl^3,4, Klaus Lehnertz^5,6,7

¹Department of Epileptology, University Hospital Bonn, Venusberg Campus 1, 53127, Bonn, Germany. thorsten.rings@uni-bonn.de.

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Summary

Functional networks derived from time-series analysis closely match structural network properties, especially key node centralities. However, global network characteristics like clustering and synchronizability show significant deviations, highlighting the need for refined analysis of complex systems.

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Area of Science:

Complex Systems Science
Network Science
Dynamical Systems Theory

Background:

Complex dynamical systems are often modeled as networks, with vertices representing units and edges representing couplings.
When structural network edges are inaccessible, functional networks are derived from vertex interactions, but their correspondence to structural properties remains unclear.

Purpose of the Study:

To investigate the extent to which functional network properties match those of the underlying structural network.
To analyze the relationship between structure and function in complex dynamical systems using time-series analysis.

Main Methods:

Derivation of functional networks from characterizing interactions in paradigmatic oscillator networks.
Application of widely-used time-series analysis techniques to study collective network dynamics.
Evaluation of key network constituents (betweenness, eigenvector centrality) and global topological/spectral properties (clustering coefficient, average shortest path length, assortativity, synchronizability).

Main Results:

Key functional network constituents, specifically betweenness and eigenvector centrality, show high congruence with structural network ground truth.
Global topological and spectral properties of functional networks, including clustering coefficient, average shortest path length, assortativity, and synchronizability, significantly deviate from structural counterparts.
Similar findings were observed for an empirical network, confirming the robustness of the results.

Conclusions:

Functional networks derived from time-series data can accurately capture local structural properties, particularly node importance.
Global network properties derived from functional data may not reliably reflect the underlying structural network.
Findings necessitate conceptual and methodological refinements for a deeper understanding of structure-function relationships in complex dynamical systems.