Detrended Fluctuation Analysis on Correlations of Complex Networks Under Attack and Repair Strategy

<正> We analyze the correlation properties of the Erd(o|¨)s-Rényi random graph(RG)and the Barabási-Albertscale-free network(SF)under the attack and repair strategy with detrended fluctuation analysis(DFA).The maximumdegree k_(max),representing the local property of the system,shows similar scaling behaviors for random graphs andscale-free networks.The fluctuations are quite random at short time scales but display strong anticorrelation at longertime scales under the same system size N and different repair probability p_(re).The average degree〈k〉,revealing thestatistical property of the system,exhibits completely different scaling behaviors for random graphs and scale-freenetworks.Random graphs display long-range power-law correlations.Scale-free networks are uncorrelated at short timescales;while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of p_(re·)

We analyze the correlation properties of the Erd6s-Rdnyi random graph （RG） and the Barabdsi-Albert scale-free network （SF） under the attack and repair strategy with detrended fluctuation analysis （DFA）. The maximum degree kmax, 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 pre. The average degree 〈k〉, 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 pre.