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Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks
Various real-life networks exhibit degree correlations and heterogeneous
structure, with the latter being characterized by power-law degree distribution
, where the degree exponent 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 , with an aim to explore the
impacts of structure heterogeneity on APL and RWs. We show that the degree
exponent has no effect on APL of RSFTs: In the full range of
, behaves as a logarithmic scaling with the number of network nodes
(i.e. ), which is in sharp contrast to the well-known double
logarithmic scaling () previously obtained for uncorrelated
scale-free networks with . In addition, we present that some
scaling efficiency exponents of random walks are reliant on degree exponent
.Comment: The definitive verion published in Journal of Mathematical Physic
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