  We propose a new measure to characterize the dimension of complex networks
based on the ergodic theory of dynamical systems. This measure is derived from
the correlation sum of a trajectory generated by a random walker navigating the
network, and extends the classical Grassberger-Procaccia algorithm to the
context of complex networks. The method is validated with reliable results for
both synthetic networks and real-world networks such as the world
air-transportation network or urban networks, and provides a computationally
fast way for estimating the dimensionality of networks which only relies on the
local information provided by the walkers.
