Many studies have shown that we can gain additional information on time
series by investigating their accompanying complex networks. In this work, we
investigate the fundamental topological and fractal properties of recurrence
networks constructed from fractional Brownian motions (FBMs). First, our
results indicate that the constructed recurrence networks have exponential
degree distributions; the relationship between H and canberepresentedbyacubicpolynomialfunction.Wenextfocusonthemotifrankdistributionofrecurrencenetworks,sothatwecanbetterunderstandnetworksatthelocalstructurelevel.Wefindtheinterestingsuperfamilyphenomenon,i.e.therecurrencenetworkswiththesamemotifrankpatternbeinggroupedintotwosuperfamilies.Last,wenumericallyanalyzethefractalandmultifractalpropertiesofrecurrencenetworks.Wefindthattheaveragefractaldimension of recurrence networks decreases with the Hurst
index H of the associated FBMs, and their dependence approximately satisfies
the linear formula ≈2−H. Moreover, our numerical results of
multifractal analysis show that the multifractality exists in these recurrence
networks, and the multifractality of these networks becomes stronger at first
and then weaker when the Hurst index of the associated time series becomes
larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst
index H=0.5 possess the strongest multifractality. In addition, the
dependence relationships of the average information dimension andtheaveragecorrelationdimension on the Hurst index H can also be
fitted well with linear functions. Our results strongly suggest that the
recurrence network inherits the basic characteristic and the fractal nature of
the associated FBM series.Comment: 25 pages, 1 table, 15 figures. accepted by Phys. Rev.