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Underlying scale-free trees in complex networks

Kim, Dong-Hee and Son, Seung-Woo and Ahn, Yong-Yeol and Kim, P.-J. and Eom, Young-Ho and Jeong, Hawoong Underlying scale-free trees in complex networks. Progress of Theoretical Physics Supplement, 157. pp. 213-220. ISSN 0375-9687 (2005)

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We investigate the properties of two relatively different spanning trees of complex networks, so-called “communication kernel" and “response network". First, for the communication kernel, we construct spanning trees carrying a maximum total weight of edges that is given by average traffic, which is defined as edge betweenness centrality. It is found that the resulting spanning tree plays an important role in communication between vertices. We also find that the degree distribution of spanning trees shows scale-free behavior for many model and real-world networks and the degree of the spanning trees has strong correlation with their original network topology. For the response network, we launch an attack on a single vertex which can drastically change the communication pattern between vertices of networks. By using minimum spanning tree technique, we construct the response network based on the measurement of the betweenness centrality changes due to a vertex removal. We find that the degree distribution of the response network indicates the scale-free behavior as well as that of the communication kernel. Interestingly, these two minimum spanning trees from different methods not only have same scale-free behavior but overlap each other in their structures. This fact indicates that the complex network has a concrete skeleton, scale-free tree, as a basic structure.

Item Type: Article
Identification Number: 10.1143/PTPS.157.213
Subjects: Q Science > QC Physics
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 02 Dec 2014 14:12
Last Modified: 18 Dec 2014 13:57
URI: http://eprints.imtlucca.it/id/eprint/2378

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