Measuring the dimension of partially embedded networks

作者：Kondor Daniel^*; Matray Peter; Csabai Istvan; Vattay Gabor

来源：Physica A: Statistical Mechanics and Its Applications , 2013, 392(18): 4160-4171.

DOI：10.1016/j.physa.2013.04.046

• Dimension measurement
• Complex network
• Spectral dimension
• Diffusion on networks

Scaling phenomena have been intensively studied during the past decade in the context of complex networks. As part of these works, recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks. In this paper we propose a new dimension measurement method for networks, which does not require global knowledge on the embedding of the nodes, instead it exploits link-wise information (link lengths, link delays or other physical quantities). Our method can be regarded as a generalization of the spectral dimension, that grasps the network's large-scale structure through local observations made by a random walker while traversing the links. We apply the presented method to synthetic and real-world networks, including road maps, the Internet infrastructure and the Gowalla geosocial network. We analyze the theoretically and empirically designated case when the length distribution of the links has the form P(rho) similar to 1/rho. We show that while previous dimension concepts are not applicable in this case, the new dimension measure still exhibits scaling with two distinct scaling regimes. Our observations suggest that the link length distribution is not sufficient in itself to entirely control the dimensionality of complex networks, and we show that the proposed measure provides information that complements other known measures.

• 出版日期2013-9-15