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We introduce Tsallis mapping in Bianconi-Barab\'asi (B-B) fitness model ofgrowing networks. This mapping addresses the dynamical behavior of the fitnessmodel within the framework of nonextensive statistics mechanics, which ischaracterized by a dimensionless nonextensivity parameter $q$. It is found thatthis new phenomenological parameter plays an important role in the evolution ofnetworks: the underlying evolving networks may undergo a different phasesdepending on the $q$ exponents, comparing to the original B-B fitness model,and the corresponding critical transition "temperature" is identified.

Tsallis mapping in growing complex networks with fitness