Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy

Details Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy

2005-08-25

arxiv.org/abs/cond-mat/0508596v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures

Scientific paper

We analyze the correlation properties of the Erdos-Renyi random graph (RG) and the Barabasi-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k_max, representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability p_re. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of p_re.

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