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Random walks and diameter of finite scale-free networks
Authors:Sungmin Lee  Yup Kim
Institution:Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Republic of Korea
Abstract:Dynamical scalings for the end-to-end distance Ree and the number of distinct visited nodes Nv of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈Ree〉 shows the dynamical scaling behavior View the MathML source, where View the MathML source is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, View the MathML source in the limit t satisfies the relation View the MathML source, where d is the diameter of network with View the MathML source for γ≥3 or View the MathML source for γ<3. Based on the scaling relation 〈Ree〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.
Keywords:05  40  Fb  89  75  Fb  89  75  Hc  05  90  +m
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