  We investigate the scaling of the cross-correlations calculated for
two-variable time series containing vertex properties in the context of complex
networks. 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 the
topological role of vertices in a given network. In order to reveal the
relation between these quantities, we applied the multifractal
cross-correlation analysis technique, which provides information about the
nonlinear effects in coupling of time series. We show that the considered
network models are characterized by unique multifractal properties of the
cross-correlation. In particular, it is possible to distinguish between
Erd\"{o}s-R\'{e}nyi, Barab\'{a}si-Albert, and Watts-Strogatz networks on the
basis of fractal cross-correlation. Moreover, the analysis of protein contact
networks reveals characteristics shared with both scale-free and small-world
models.
