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It is becoming more and more clear that complex networks present remarkablelarge fluctuations. These fluctuations may manifest differently according tothe given model. In this paper we re-consider hidden variable models which turnout to be more analytically treatable and for which we have recently shownclear evidence of non-self averaging; the density of a motif being subject topossible uncontrollable fluctuations in the infinite size limit. Here weprovide full detailed calculations and we show that large fluctuations are onlydue to the node hidden variables variability while, in ensembles where theseare frozen, fluctuations are negligible in the thermodynamic limit, and equalthe fluctuations of classical random graphs. A special attention is paid to thechoice of the cut-off: we show that in hidden-variable models, only a cut-offgrowing as $N^\lambda$ with $\lambda\geq 1$ can reproduce the scaling of apower-law degree distribution. In turn, it is this large cut-off that generatesnon-self-averaging.

Fluctuations analysis in complex networks modeled by hidden variable models. Necessity of a large cut-off in hidden-variable models