Fluctuation analysis in complex networks modeled by hidden-variable models: necessity of a large cutoff in
1Cooperative Association for Internet Data Analysis, University of California San Diego, San Diego, California, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
Summary
Complex networks exhibit large fluctuations due to hidden variables. Freezing these variables makes fluctuations negligible, similar to classical random graphs, revealing non-self-averaging properties.
Area of Science:
- Complex systems
- Network science
- Statistical physics
Background:
- Complex networks often display significant fluctuations.
- Hidden-variable models offer analytical tractability for studying network properties.
- Non-self-averaging in motif densities has been recently observed in these models.
Purpose of the Study:
- To provide detailed calculations for hidden-variable models.
- To identify the source of large fluctuations in these networks.
- To investigate the role of cutoffs in reproducing power-law degree distributions and non-self-averaging.
Main Methods:
- Detailed analytical calculations within hidden-variable models.
- Analysis of fluctuations in ensembles with frozen versus variable node-hidden variables.
- Investigation of different cutoff functions and their impact on degree distribution scaling.
Main Results:
- Large fluctuations in hidden-variable models stem solely from node-hidden variable variability.
- In frozen ensembles, fluctuations become negligible in the thermodynamic limit, matching classical random graphs.
- A cutoff scaling as N(λ) with λ ≥ 1 is necessary to reproduce power-law degree distributions and non-self-averaging.
Conclusions:
- Node-hidden variable variability is the primary driver of non-self-averaging in these complex network models.
- The choice of a growing cutoff is crucial for capturing essential scaling properties like power-law degree distributions.
- Understanding these fluctuations is key to accurately modeling complex network behavior.
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