  We propose a fluctuation analysis to quantify spatial correlations in complex
networks. The approach considers the sequences of degrees along shortest paths
in the networks and quantifies the fluctuations in analogy to time series. In
this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation
transition, a fractal network model, and examples of real-world networks are
studied. While the fluctuation functions for the BA model show exponential
decay, in the case of the Cayley tree and the fractal network model the
fluctuation functions display a power-law behavior. The fractal network model
comprises long-range anti-correlations. The results suggest that the
fluctuation exponent provides complementary information to the fractal
dimension.
