Europhys. Lett.
Volume 73, Number 4, February 2006
Page(s) 649 - 655
Section Interdisciplinary physics and related areas of science and technology
Published online 11 January 2006
Europhys. Lett., 73 (4), pp. 649-655 (2006)
DOI: 10.1209/epl/i2005-10441-3

Spectral scaling and good expansion properties in complex networks

E. Estrada

Complex Systems Research Group, X-ray Unit, RIAIDT, Edificio CACTUS University of Santiago de Compostela - 15782 Santiago de Compostela, Spain

received 30 September 2005; accepted in final form 2 January 2006
published online 11 January 2006

The existence of a scaling between the principal eigenvector and the subgraph centrality of a complex network indicates that the network has "good expansion" (GE) properties. GE is the important but counterintuitive property of being both sparsely populated and highly connected. We have detected GE properties in half of the 16 real-world networks studied, which include communication, information and biological networks. Most of social networks studied do not show GE properties as a consequence of the existence of communities with low number of inter-community links. However, the majority of food webs represent ecosystems that are not composed of separate communities with low interconnections among them and possess GE properties.

89.75.Fb - Structure and organization in complex systems.
89.75.Da - Systems obeying scaling laws.
89.75.Hc - Networks and genealogical trees.

© EDP Sciences 2006