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Percolation on correlated networks.

A V Goltsev¹, S N Dorogovtsev, J F F Mendes

¹Departamento de Física, Universidade de Aveiro, 3810-193 Aveiro, Portugal and A.F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 31, 2008

Summary

This summary is machine-generated.

This study examines percolation on random networks, finding that degree correlations can be irrelevant to critical behavior. New critical exponents emerge in networks with assortative and disassortative mixing.

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Area of Science:

Network Science
Statistical Physics
Complex Systems

Background:

Percolation theory studies the formation of connected components in random graphs.
Degree-degree correlations, linking vertex degrees of connected neighbors, influence network properties.
Understanding critical phenomena in correlated networks is crucial for diverse applications.

Purpose of the Study:

To analyze percolation on equilibrium random networks with nearest-neighbor degree-degree correlations.
To identify criteria for degree-degree correlations becoming irrelevant for critical singularities.
To explore unusual percolation behaviors and new critical exponents in assortative and disassortative networks.

Main Methods:

Revisiting percolation theory on equilibrium random networks.
Analyzing the impact of degree-degree correlations on critical singularities.
Investigating network models exhibiting assortative and disassortative mixing.

Main Results:

Established criteria for degree-degree correlations to be irrelevant for critical singularities.
Demonstrated that specific correlations do not alter critical behavior.
Identified novel percolation properties and critical exponents in correlated networks.

Conclusions:

Degree-degree correlations can be irrelevant to critical singularities in certain random networks.
Assortative and disassortative mixing can lead to unique percolation phenomena.
The study reveals new insights into critical exponents in complex network structures.