Spectral scaling and good expansion properties in complex networks

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: 2 January 2006

Abstract

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.