Regensburg 2010 – wissenschaftliches Programm
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BP: Fachverband Biologische Physik
BP 24: Networks: From Topology to Dynamics III (joint DY, BP, SOE)
BP 24.3: Vortrag
Donnerstag, 25. März 2010, 10:45–11:00, H44
Large-deviation properties of random graphs — •Alexander K. Hartmann — Institut of Physics, University of Oldenburg
The large-deviation properties of different types of random graphs are studied using numerical simulations. In particular the number of components and the graph diameter are considered. The distributions of these quantities are obtained down to very small probabilities like 10−700 using finite-temperature Monte Carlo and Wang Landau simulations. Different graphs ensembles as Erdös-Renyi, small-world and scale-free graphs are studied as a function of suitable control parameters. The parameter-dependend changes of the distributions are recorded, indicating the presence of non-standard transitions.
In particular, the distributions of the diameter are often given by Gumbel distributions, except right at a percolation transition, or are very close to Gumbel distributions.