Percolation of a random network by statistical physics method

Hai Lin () and Jingcheng Wang
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Hai Lin: Department of Automation, Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, P. R. China
Jingcheng Wang: Department of Automation, Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, P. R. China†Autonomous Systems and Intelligent Control, International Joint Research Center, Xian Technological University, Xian 710021, P. R. China

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 02n03, 1-17

Abstract: In this paper, we develop an analytical framework and analyze the percolation properties of a random network by introducing statistical physics method. To adequately apply the statistical physics method on the research of a random network, we establish an exact mapping relation between a random network and Ising model. Based on the mapping relation and random cluster model (RCM), we obtain the partition function of the random network and use it to compute the size of the giant component and the critical value of the present probability. We extend this approach to investigate the size of remaining giant component and the critical phenomenon in the random network which is under a certain random attack. Numerical simulations show that our approach is accurate and effective.

Keywords: Statistical physics method; complex networks; random cluster model; giant component (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0129183119500098

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