Abstract
We analyze the correlation properties of the Erdös–Rényirandom graph (RG) and the Barabási–Albert scale-free network(SF) under the attack and repair strategy with detrendedfluctuation analysis (DFA). The maximum degree kmax,representing the local property of the system, shows similarscaling behaviors for random graphs and scale-free networks. Thefluctuations are quite random at short time scales but displaystrong anticorrelation at longer time scales under the same systemsize N and different repair probability pre. The averagedegree ⟨k⟩, revealing the statistical property ofthe system, exhibits completely different scaling behaviors forrandom graphs and scale-free networks. Random graphs displaylong-range power-law correlations. Scale-free networks areuncorrelated at short time scales; while anticorrelated at longertime scales and the anticorrelation becoming stronger with theincrease of pre.
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