Dimension of spatially embedded networks

Li Daqing, Kosmas Kosmidis, Armin Bunde, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

190 Scopus citations


The dimension of a system is one of the most fundamental quantities to characterize its structure and basic physical properties. Diffusion and vibrational excitations, for example, as well as the universal features of a system near a critical point depend crucially on its dimension. However, in the theory of complex networks the concept of dimension has been rarely discussed. Here we study models for spatially embedded networks and show how their dimension can be determined. Our results indicate that networks characterized by a broad distribution of link lengths have a dimension higher than that of the embedding space. We illustrate our findings using the global airline network and the Internet and argue that although these networks are embedded in two-dimensional space they should be regarded as systems with dimension close to 3 and 4.5, respectively. We show that the network dimension is a key concept to understand not only network topology, but also dynamical processes on networks, such as diffusion and critical phenomena including percolation.

Original languageEnglish
Pages (from-to)481-484
Number of pages4
JournalNature Physics
Issue number6
StatePublished - Jun 2011

Bibliographical note

Funding Information:
We thank ONR, DTRA, Deutsche Forschungsgemeinschaft (DFG), the Israel Science Foundation, and the European Project EPIWORK for financial support.


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