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Author Zhang, Zhongzhi ♦ Zhang, Yichao ♦ Zhou, Shuigeng ♦ Yin, Ming ♦ Guan, Jihong
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-09-14
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics
Subject Keyword Physics - Physics and Society ♦ Condensed Matter - Statistical Mechanics ♦ physics:cond-mat ♦ physics:physics
Abstract Various real-life networks exhibit degree correlations and heterogeneous structure, with the latter being characterized by power-law degree distribution $P(k)\sim k^{-\gamma}$, where the degree exponent $\gamma$ describes the extent of heterogeneity. In this paper, we study analytically the average path length (APL) of and random walks (RWs) on a family of deterministic networks, recursive scale-free trees (RSFTs), with negative degree correlations and various $\gamma \in (2,1+\frac{\ln 3}{\ln 2}]$, with an aim to explore the impacts of structure heterogeneity on APL and RWs. We show that the degree exponent $\gamma$ has no effect on APL $d$ of RSFTs: In the full range of $\gamma$, $d$ behaves as a logarithmic scaling with the number of network nodes $N$ (i.e. $d \sim \ln N$), which is in sharp contrast to the well-known double logarithmic scaling ($d \sim \ln \ln N$) previously obtained for uncorrelated scale-free networks with $2 \leq \gamma <3$. In addition, we present that some scaling efficiency exponents of random walks are reliant on degree exponent $\gamma$.
Description Reference: Journal of Mathematical Physics 50, 033514 (2009)
Educational Use Research
Learning Resource Type Article


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