2009 Volume 78 Issue 12 Pages 124002
The generalized Gumbel distribution function (GGDF) has been conjectured to describe fluctuating order parameters of a large class of finite critical systems. We study probability distribution functions (PDFs) of rescaled order parameters in finite complex networks near their critical points to clarify whether this conjecture holds for any critical system. Our numerical results show that the PDF for fitness-model networks near the critical point, which has the scale-free property, cannot be described by the GGDF with the real parameter a equal to π⁄2 while the PDF for non-scale-free Erdos–Rényi random graphs obeys it. We also discuss the origin of the discrepancy with the GGDF in the scale-free network.
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