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We investigate the scaling of the cross-correlations calculated fortwo-variable time series containing vertex properties in the context of complexnetworks. Time series of such observables are obtained by means of stationary,unbiased random walks. We consider three vertex properties that provide,respectively, short, medium, and long-range information regarding thetopological role of vertices in a given network. In order to reveal therelation between these quantities, we applied the multifractalcross-correlation analysis technique, which provides information about thenonlinear effects in coupling of time series. We show that the considerednetwork models are characterized by unique multifractal properties of thecross-correlation. In particular, it is possible to distinguish betweenErd\"{o}s-R\'{e}nyi, Barab\'{a}si-Albert, and Watts-Strogatz networks on thebasis of fractal cross-correlation. Moreover, the analysis of protein contactnetworks reveals characteristics shared with both scale-free and small-worldmodels.

Multifractal cross-correlation effects in two-variable time series of complex network vertex observables