Analytic formula for hidden variable distribution: Complex networks arising from fluctuating random graphs

Details Analytic formula for hidden variable distribution: Complex networks arising from fluctuating random graphs Analytic formula for hidden variable distribution: Complex networks arising from fluctuating random graphs

2005-01-18

arxiv.org/abs/cond-mat/0501429v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages and 1 figure

Scientific paper

In analogy to superstatistics, which connects Boltzmann-Gibbs statistical mechanics to its generalizations through temperature fluctuations, complex networks are constructed from the fluctuating Erdos-Renyi random graphs. Here, using the quantum mechanical method, the exact analytic formula is presented for the hidden variable distribution, which describes the fluctuation and generates a generic degree distribution through the Poisson transformation. As an example, a static scale-free network is discussed and the corresponding hidden variable distribution is found to decay as a power law.

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