Disassortativity of percolating clusters in random networks

Shogo Mizutaka and Takehisa Hasegawa
Phys. Rev. E 98, 062314 – Published 18 December 2018

Abstract

We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the assortativity of a giant component, r, which is defined as Pearson's correlation coefficient for degrees of directly connected nodes. For uncorrelated random networks in which the third moment for the degree distribution is finite, we prove the following two points: (1) Assortativity r satisfies the relation r0 for ppc. (2) The average degree of nodes adjacent to degree k nodes at the percolation threshold is proportional to k1 independently of the degree distribution function. These results claim that disassortativity emerges in giant components near the percolation threshold. The accuracy of the analytical treatment is confirmed by extensive Monte Carlo simulations.

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  • Received 25 July 2018

DOI:https://doi.org/10.1103/PhysRevE.98.062314

©2018 American Physical Society

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Authors & Affiliations

Shogo Mizutaka* and Takehisa Hasegawa

  • Department of Mathematics and Informatics, Ibaraki University, 2-1-1 Bunkyo, Mito 310-8512, Japan

  • *shogo.mizutaka.sci@vc.ibaraki.ac.jp
  • takehisa.hasegawa.sci@vc.ibaraki.ac.jp

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Issue

Vol. 98, Iss. 6 — December 2018

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