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Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
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Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Published on: September 25, 2021

Core percolation on complex networks.

Yang-Yu Liu1, Endre Csóka, Haijun Zhou

  • 1Center for Complex Network Research and Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA. ya.liu@neu.edu

Physical Review Letters
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

Complex networks lack a core if purely scale-free. Core percolation transitions differ between directed and undirected networks, with distinct critical behaviors observed.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • The core of a complex network is a fundamental subgraph crucial for network robustness and function.
  • Understanding percolation transitions, especially in networks with heterogeneous degree distributions, is vital for network analysis.

Purpose of the Study:

  • To analytically solve the core percolation problem for complex networks with arbitrary degree distributions.
  • To investigate the existence and nature of the core in scale-free networks.
  • To compare core percolation behavior in directed versus undirected networks.

Main Methods:

  • Analytical solution of the core percolation problem.
  • Analysis of arbitrary degree distributions in complex networks.
  • Investigation of critical exponents and percolation transition types (continuous, discontinuous, hybrid).

Main Results:

  • Purely scale-free networks exhibit no core, irrespective of degree exponents.
  • Core percolation in undirected networks is continuous.
  • Core percolation in directed networks is discontinuous and hybrid when in- and out-degree distributions differ.
  • Distinct critical exponents characterize core percolation in undirected and directed networks.

Conclusions:

  • The presence and behavior of a network's core are highly dependent on its degree distribution and directedness.
  • Scale-free network properties fundamentally alter core percolation dynamics.
  • The analytical framework provides new insights into network resilience and structure.