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Correlation Dimension of Complex Networks
Lacasa Saiz de Arce, Lucas and Gómez-Gardeñes, Jesús
Correlation Dimension of Complex Networks.
"Physical Review Letters", v. 110
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.
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