The mixed assortativity property of finite Barabasi-Albert networks and its influence on diffusion times
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In spite of the large number of existing studies on Barabasi-Albert (BA) networks, their two-point correlation functions have been completely analysed only recently by Fotouhi and Rabbatn , who have given the full expressions of the conditional probabilities P(hjk) in the large network limit for any value of the parameter b (the number of child nodes in the preferential attachment process). Concerning the assortativity properties of these networks, in previous work some estimates of the Newman coefficient r were found . According to these estimates, for large N (number of nodes), r vanishes as lnN=N . It was therefore generally believed that BA networks are almost uncorrelated, and numerical simulations appeared to confirm this. However, more recent asymptotic estimates [3, 4] yield a different result: r vanishes only as - ln N/N for large N. It should be recalled that for real networks with the same scale-free exponent (g = 3), the r coefficient is always small in absolute value, so even this small total disassortativity is significant.