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Open networks in discrete time: Passing vs blocking behavior.

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This study introduces a framework to analyze how discrete-time complex networks pass or block external signals. A new network index reveals structural signatures influencing information flow in biological, technological, and ecological systems.

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Area of Science:

  • Network Science
  • Systems Theory
  • Control Theory

Background:

  • Complex networks are often modeled in discrete time, including opinion dynamics, Markov chains, and diffusion processes.
  • Understanding how these networks interact with their environment as open systems is crucial for analyzing information flow.
  • Existing methods may not efficiently characterize the input-output behavior of discrete-time complex networks.

Purpose of the Study:

  • To develop a unified framework for analyzing the input-output behavior of discrete-time complex networks as open systems.
  • To characterize whether these networks amplify (pass) or suppress (block) external inputs.
  • To provide a computationally efficient method for comparing network topologies based on their signal processing capabilities.

Main Methods:

  • Combining the network's transfer function with the discrete-time controllability Gramian.
  • Utilizing the H2-norm to measure signal gain across diverse input types.
  • Introducing a network index based on Gramian trace and eigenvalues for scalable analysis.

Main Results:

  • A general framework is established for characterizing signal amplification or suppression in discrete-time networks.
  • A computationally efficient network index is developed, enabling scalable comparisons of network topologies.
  • Empirical networks across biological, technological, and ecological domains exhibit consistent structural signatures related to passing or blocking behavior.

Conclusions:

  • The developed framework effectively analyzes the input-output dynamics of discrete-time complex networks.
  • Network architecture and the choice of input/output nodes significantly shape information flow.
  • Findings have broad implications for network control, signal processing, and the design of complex systems.