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Dynamics on modular networks with heterogeneous correlations.

Sergey Melnik1, Mason A Porter2, Peter J Mucha3

  • 1MACSI, Department of Mathematics & Statistics, University of Limerick, Ireland.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

We introduce a novel modular random graph model allowing distinct degree-degree correlations within modules. This flexible network ensemble enables analysis of complex dynamics on interconnected systems.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Modular random graphs are crucial for modeling complex systems.
  • Existing models often assume uniform correlations within modules.
  • Understanding inter-module connections is key to network behavior.

Purpose of the Study:

  • To develop a new ensemble of modular random graphs with heterogeneous intra-module degree-degree correlations.
  • To introduce an analytical framework for studying dynamics on these complex networks.
  • To generalize existing network models for more realistic interconnected systems.

Main Methods:

  • Development of a novel modular random graph ensemble.
  • Formulation of an analytical approach for binary dynamics analysis.
  • Application of the approach to bond percolation, site percolation, and the Watts threshold model.

Main Results:

  • The proposed network ensemble allows for varying degree-degree correlations across different modules.
  • Inter-module connections are governed by joint degree-degree distributions between module pairs.
  • The analytical framework successfully analyzes percolation and threshold models on the new network ensemble.

Conclusions:

  • The new network ensemble provides a more flexible and realistic representation of modular complex systems.
  • The analytical approach facilitates the study of network dynamics in systems with heterogeneous modular structures.
  • This work generalizes existing random graph models, enabling analysis of non-identical interacting networks.