Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution.
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.
Abe
Sumiyoshi
S
Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan. suabe@sf6.so-net.ne.jp
Thurner
Stefan
S
D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009716:Numerical Analysis, Computer-Assisted; D016008:Statistical Distributions; D009435:Synaptic Transmission / Q000502:physiology*