title: Fluctuation analysis in complex networks modeled by hidden-variable models: necessity of a large cutoff in hidden-variable models.
abstract: It is becoming more and more clear that complex networks present remarkable large fluctuations. These fluctuations may manifest differently according to the given model. In this paper we reconsider hidden-variable models which turn out to be more analytically treatable and for which we have recently shown clear evidence of non-self-averaging, the density of a motif being subject to possible uncontrollable fluctuations in the infinite-size limit. Here we provide full detailed calculations and we show that large fluctuations are only due to the node-hidden variables variability while, in ensembles where these are frozen, fluctuations are negligible in the thermodynamic limit and equal the fluctuations of classical random graphs. A special attention is paid to the choice of the cutoff: We show that in hidden-variable models, only a cutoff growing as N(λ) with λ ≥ 1 can reproduce the scaling of a power-law degree distribution. In turn, it is this large cutoff that generates non-self-averaging.
authors.affiliation: Cooperative Association for Internet Data Analysis, University of California San Diego, San Diego, California, USA.
authors.forename: Massimo
authors.initials: M
authors.lastname: Ostilli
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D053858:Metabolic Networks and Pathways / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical