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

摘要

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·)