Classification of transport backbones of complex networks.
Transport properties in random and scale-free (SF) networks are studied by analyzing the betweenness centrality (BC) distribution P(B) in the minimum spanning trees (MSTs) and infinite incipient percolation clusters (IIPCs) of the networks. It is found that P(B) in MSTs scales as P(B)∼B(-δ). The obtained values of δ are classified into two different categories, δ≃1.6 and δ≃2.0. Using the mapping between BC and the branch size of tree structures, it is proved that δ in MSTs which are close to critical trees is 1.6. In contrast, δ in MSTs which are supercritical trees is shown to be 2.0. We also find δ=1.5 in IIPCs, which is a natural result because IIPC is physically critical. Based on the results in MSTs, a physical reason why δ≥2 in the original networks is suggested.
Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
Woosik
W
Choi
Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
Huiseung
H
Chae
Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
Soon-Hyung
SH
Yook
Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
Yup
Y
Kim