Journal of the Physical Society of Japan
Online ISSN : 1347-4073
Print ISSN : 0031-9015
ISSN-L : 0031-9015
Fluctuations of the Order Parameter in Critical Complex Networks
Mutsumi MitobeKousuke Yakubo
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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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© The Physical Society of Japan 2009
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