Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks

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dc.creatorZhang, Zhongzhi
dc.creatorZhang, Yichao
dc.creatorZhou, Shuigeng
dc.creatorYin, Ming
dc.creatorGuan, Jihong
dc.date2008-09-14
dc.date2009-03-31
dc.date.accessioned2026-07-07T12:57:58Z
dc.date.available2026-07-07T12:57:58Z
dc.descriptionVarious real-life networks exhibit degree correlations and heterogeneous structure, with the latter being characterized by power-law degree distribution $P(k)\sim k^{-γ}$, where the degree exponent $γ$ 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 $γ\in (2,1+\frac{\ln 3}{\ln 2}]$, with an aim to explore the impacts of structure heterogeneity on APL and RWs. We show that the degree exponent $γ$ has no effect on APL $d$ of RSFTs: In the full range of $γ$, $d$ 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 $2 \leq γ<3$. In addition, we present that some scaling efficiency exponents of random walks are reliant on degree exponent $γ$.
dc.descriptionThe definitive verion published in Journal of Mathematical Physics
dc.identifierhttps://arxiv.org/abs/0809.2384
dc.identifierhttp://arxiv.org/abs/0809.2384
dc.identifierJournal of Mathematical Physics 50, 033514 (2009)
dc.identifierdoi:10.1063/1.3094757
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225090
dc.subjectPhysics and Society
dc.subjectStatistical Mechanics
dc.titleInfluences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks
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