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

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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