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Correlated edge overlaps in multiplex networks.

Gareth J Baxter1, Ginestra Bianconi2, Rui A da Costa1

  • 1Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.

Physical Review. E
|August 31, 2016
PubMed
Summary
This summary is machine-generated.

We introduce a theory for sparse multiplex networks, revealing how link correlations impact network structure and phase transitions. This work identifies key factors influencing the giant mutually connected component in complex systems.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Multiplex networks, with layers of interconnected nodes, are crucial for modeling real-world systems.
  • Understanding the behavior of these networks, especially with overlapping links, is a significant challenge.
  • Local network properties, like treelikeness, can offer insights into global network behavior.

Purpose of the Study:

  • To develop a theoretical framework for analyzing sparse multiplex networks with partially overlapping links.
  • To investigate the influence of correlations between different link types on network structure.
  • To identify and characterize the giant mutually connected component in such systems.

Main Methods:

  • Developing a theory based on the local treelikeness of sparse multiplex networks.
  • Analyzing two-layer multiplex networks with arbitrary correlations between connections.
  • Mapping the phase diagram of the system under varying correlation conditions.

Main Results:

  • The developed theory successfully identifies the giant mutually connected component.
  • Correlations between overlapping and nonoverlapping links significantly alter the system's phase diagram.
  • Multiple hybrid phase transitions are observed due to these correlations.
  • Recurrent hybrid phase transitions are specifically found for assortative correlations.

Conclusions:

  • Local treelikeness provides a powerful tool for understanding sparse multiplex networks.
  • Link correlations are critical determinants of the phase transitions and connectivity in multiplex networks.
  • The findings offer new insights into the structure and behavior of complex, multilayered systems.