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Explicit and implicit network connectivity: Analytical formulation and application to transport processes.

Enrico Ser-Giacomi1, Térence Legrand2, Ismael Hernández-Carrasco3

  • 1Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 54-1514 MIT, Cambridge, Massachusetts 02139, USA.

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Summary
This summary is machine-generated.

We developed a new analytical method to calculate network connectivity probabilities for any path length in complex networks. This approach reveals how transport structures influence connectivity, offering insights into ocean currents and seascape dynamics.

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Area of Science:

  • Network Science
  • Complex Systems
  • Mathematical Physics

Background:

  • Network connectivity is crucial for dynamics but lacks analytical methods for varying path lengths.
  • Understanding connectivity in temporal, directed, and weighted networks is essential for modeling real-world systems.

Purpose of the Study:

  • To derive exact expressions for random-walk connectivity probabilities in generic networks.
  • To characterize explicit and implicit connectivity through causal paths and network motifs.
  • To establish a framework for assessing transport dynamics based on connectivity probabilities.

Main Methods:

  • Derivation of exact analytical expressions for connectivity probabilities.
  • Analysis of random-walk processes on temporal, directed, and weighted networks.
  • Application of the theoretical framework to oceanographic transport data.

Main Results:

  • Novel exact formulas for connectivity probabilities across arbitrary path lengths.
  • Identification of connectivity patterns influenced by network motifs (pitchforks).
  • Demonstration of the framework's utility in analyzing ocean transport, revealing fluid barriers and corridors.

Conclusions:

  • The derived framework provides a powerful tool for understanding network connectivity and transport dynamics.
  • Ocean transport exhibits complex connectivity patterns shaped by large-scale structures like barriers and corridors.
  • This research offers novel insights into seascape connectivity driven by ocean currents.