PMID- 32255840 OWN - NLM STAT- PubMed-not-MEDLINE LR - 20200928 IS - 0022-2488 (Print) IS - 1089-7658 (Electronic) IS - 0022-2488 (Linking) VI - 50 IP - 3 DP - 2009 Mar TI - Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks. PG - 033514 LID - 10.1063/1.3094757 [doi] LID - 033514 AB - Various real-life networks exhibit degree correlations and heterogeneous structure, with the latter being characterized by power-law degree distribution P(k) approximately 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 ∊ (2, 1 + ln 3/ln 2] , with an aim to explore the impacts of structure heterogeneity on the APL and RWs. We show that the degree exponent gamma has no effect on the 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 approximately ln N ), which is in sharp contrast to the well-known double logarithmic scaling (d approximately ln ln N) previously obtained for uncorrelated scale-free networks with 2