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Multiscale dynamical embeddings of complex networks.

Michael T Schaub1,2, Jean-Charles Delvenne3,4, Renaud Lambiotte5

  • 1Institute for Data, Systems and Society, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

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Summary
This summary is machine-generated.

We introduce a novel dynamical similarity measure for nodes in complex networks, enabling dimensionality reduction and functional module discovery. This method enhances understanding and control of network dynamics across various timescales.

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Area of Science:

  • Network science
  • Control theory
  • Data analysis

Background:

  • Complex systems and relational data are frequently modeled as dynamical processes on networks.
  • Understanding, predicting, and controlling network behavior necessitates extracting reduced descriptions of these networks.

Purpose of the Study:

  • To propose a time-dependent dynamical similarity measure between nodes.
  • To quantify the effect of node inputs on network dynamics.
  • To develop an embedding for dimensionality reduction and functional module discovery.

Main Methods:

  • Development of a time-dependent dynamical similarity measure inspired by control theory.
  • Induction of a node embedding based on dynamical similarity.
  • Application of embeddings for dimensionality reduction across different timescales.
  • Exploitation of embeddings for uncovering functional modules in networks.

Main Results:

  • The proposed dynamical similarity measure effectively quantifies node influence within a network.
  • The induced embedding facilitates dimensionality reduction, capturing dynamic similarities at various timescales.
  • The method successfully uncovers functional modules in directed and signed networks.
  • A generalized link between community detection and control theory is established through a dynamical perspective.

Conclusions:

  • The dynamical similarity measure provides a powerful tool for analyzing complex network dynamics.
  • This approach offers novel insights into network structure and function, particularly for challenging network types.
  • The framework bridges concepts from control theory and network analysis, paving the way for advanced network control strategies.