Quantifying the connectivity of scale-free and biological networks
نویسندگان
چکیده
Scale-free and biological networks follow a power law distribution pk / k a for the probability that a node is connected to k other nodes; the corresponding ranges for a (biological: 1 < a < 2; scale-free: 2 < a6 3) yield a diverging variance for the connectivity k and lack of predictability for the average connectivity. Predictability can be achieved with the R enyi, Tsallis and Landsberg–Vedral extended entropies and corresponding ‘‘disorders’’ for correctly chosen values of the entropy index q. Escort distributions pk / k aq with q > 3=a also yield a nondiverging variance and predictability. It is argued that the Tsallis entropies may be the appropriate quantities for the study of scale-free and biological networks. 2003 Elsevier Ltd. All rights reserved.
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