Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution.

Sumiyoshi Abe; Stefan Thurner

doi:10.1103/physreve.72.036102

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Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution.

Sumiyoshi Abe·Stefan Thurner

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Abstract

In analogy to superstatistics, which connects Boltzmann-Gibbs statistical mechanics to its generalizations through temperature fluctuations, complex networks are constructed from fluctuating Erdös-Rényi random graphs. Using a quantum-mechanical method, the exact analytic formula for the hidden variable distribution is presented which describes the nature of the fluctuations 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 and to diverge at the origin.

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Sumiyoshi Abe, Stefan Thurner. 2005-09-02. Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution.. https://doi.org/10.1103/physreve.72.036102

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